knowledge representation formalism for building semantic web … · 2018-09-21 · knowledge...

Knowledge Representation Formalism For

Building Semantic Web Ontologies

by

Basak Taylan

A survey submitted to the Graduate Faculty in Computer Science in partial

fulfillment of the requirements for the degree of Doctor of Philosophy, The

City University of New York.

2017

Contents

1 INTRODUCTION 6

2 SEMANTIC WEB 11

3 KNOWLEDGE REPRESENTATION 24

3.1 KNOWLEDGE . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 KNOWLEDGE REPRESENTATION FORMALISM . . . . . 27

3.2.1 Roles Of Knowledge Representation . . . . . . . . . . . 27

3.3 KNOWLEDGE REPRESENTATION METHODS . . . . . . . 33

3.3.1 NETWORKED REPRESENTATION . . . . . . . . . . 33

3.3.1.1 SEMANTIC NETWORKS . . . . . . . . . . 33

3.3.1.2 CONCEPTUAL GRAPHS . . . . . . . . . . 39

3.3.2 STRUCTURAL REPRESENTATION . . . . . . . . . 42

3.3.2.1 FRAMES . . . . . . . . . . . . . . . . . . . . 42

3.3.2.2 KL-ONE KNOWLEDGE REPRESENTATION

SYSTEMS . . . . . . . . . . . . . . . . . . . 49

3.3.3 LOGIC-BASED REPRESENTATION . . . . . . . . . 53

3.3.3.1 PROPOSITIONAL LOGIC(PL) . . . . . . . 54

3.3.3.2 FIRST-ORDER LOGIC(FOL) . . . . . . . . 58

2

CONTENTS 3

3.3.3.3 DESCRIPTION LOGICS . . . . . . . . . . . 64

3.3.3.4 FRAME LOGIC(F-LOGIC) . . . . . . . . . . 76

4 APPLICATIONS 86

4.1 The Open Mind Common Sense Project(OMCS) . . . . . . . . 86

4.2 ConceptNet 3: a Flexible, Multilingual Semantic Network for

Common Sense Knowledge . . . . . . . . . . . . . . . . . . . . 89

4.3 WordNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.4 FrameNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.5 VerbNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.6 The Brandeis Semantic Ontology (BSO) . . . . . . . . . . . . 107

5 CONCLUSION 109

Abstract

The initial idea of Tim Berners Lee when designing The Wold Wide Web was

creating a commonly accessible area in the network for information sharing

by means of hyperlinks without concerning about platform dependency in

late 1980s[28]. Since then, the Web has been growing dramatically and it has

became a major information retrieval means. By 2014, number of websites

reached over a billion. Looking for a particular information within these

globally connected pages can be explained by analogy with looking for a black

cat in a coal cellar. Thus, manual search within such huge network becomes

more and more difficult as the number of web pages increase. This necessity

lead adding another layer,“the meaning”, on top of the current Web. This

additional layer also known as Semantic Web, adds machine readability to

the current web pages, that are designed for human consumption. By having

machine processable data, data will be suitable for both machine and human

consumption, information will be accessed faster, and search results will be

more accurate. In addition, by being able to do inferences on the Web data,

the pieces that consists of the answer that are partially located on different

web pages can be combined and instead of referring a list of web pages, that

consists of part of the answer, the answer itself collected from different web

resources as a whole can be returned by using Semantic Web.

4

CONTENTS 5

Knowledge representation and ontology construction plays a crucial role

in order to establish such layer on top of the current Web.

In section-1, we are going to present a literature review about Web

history and evolution of the Web since its invention. In section-2, we will

introduce the Semantic Web structure. In section-3 we will present major

knowledge representation formalism and methods that influenced construction

of Ontologies for Semantic Web. In section-4, we will introduce some of the

applications that are used to build Ontologies. In section-5, we will have the

conclusion of Ontology building for Semantic Web.

Chapter 1

INTRODUCTION

The World Wide Web,“the embodiment of human knowledge[1].”, was first

proposed in 1989 by Tim Berners-Lee at the European Organization for

Nuclear Research (CERN) in Geneva. The idea of creating the web was

enabling an area in the computer that is accessible by other people. After his

proposal, Berners-Lee coded the first browser, and WEB server working on

NEXT computers[78, 18, 16, 20]. After invention of the platform independent

“line mode” browser[17] developed by Nicola Pellow in 1991, the web evolved

rapidly. The web evolution consists of three phases: web 1.0, web 2.0, web

3.0 [30].

Web 1.0, the Web of documents, includes development in The World Wide

Web within the time range between 1989 and 2005. The first generation

of the Web consists of static pages, where information was only accessed

only in “read-only” mode. Users had limited interaction with the pages.

Thus, communication was unidirectional.Web 1.0 includes core web protocols,

HTML, HTTP, and URI [32, 30, 66, 95].

6

CHAPTER 1. INTRODUCTION 7

Web 2.0, the second generation of the Web (a.k.a “the wisdom web,

people-centric web, participative web, or read-write web”), is a result of a

brainstorming session between O’Reilly and MediaLive International in a

conference. It allows users to be content creators by participation, collabora-

tion, and information sharing on the web. Since user can both read from and

write into the web pages, communication is bi-directional. Web 2.0 is differ-

ent than web 1.0 in various aspects such as technological(Ajax, JavaScript,

Cascading Style Sheets (CSS), Document Object Model (DOM), Extensible

HTML (XHTML), XSL Transformations (XSLT)/XML, and Adobe Flash),

structural(page layout) and sociological aspects(notion of friends and groups)

[32, 79, 30, 66, 95].Youtube, Flickr, personal blogs, search engines, Wikipedia,

Voice over IP, chat applications, instant messages, etc can be shown as Web

2.0 platform applications.

The World Wide Web has become irreplaceable means of accessing the

information. According to [64], The Indexed Web contains at least 4.6 billion

pages as of today (18 August 2017), and it is continuously getting larger

and larger while even this paper is being typed. In this rapidly growing

environment, accessing correct information within acceptable time limit is one

of challenges that every Internet user experiences. Technological developments

changed our way for seeking for information and most of us became dependent

on search engines. Difficulty of finding a little piece of information in such

a big environment can be explained by analogy with looking for a black

cat in a coal cellar in less than a second. Despite the many advanced

searching algorithms that are used in search engines, search engines are still

suffering from returning completely irrelevant results along with the correct

answers. One of the reasons that causes this undesired situation is that


textual or graphical resources on the Internet are designed for mostly human

consumption [9]. In addition to that, query results are independent web pages.

If we are looking for information spread over multiple pages, current web

technology falls short of satisfying our needs [4].

Web 3.0, the third generation of the Web (a.k.a “Semantic Web, executable

Web, or read-write-execute Web”), is an extension of Web 2.0, that aims to

add semantics to the Web by enabling machine processable documents [30,

66, 95, 19, 56]. Semantic Web can be considered as a globally linked database

where the information is suitable for both human and machine consumption.

Google Squared, Hakia, Walfram Alfa, IBM Watson, Browser Plugin Zemanta,

“like button” of Facebook, E-Commerce travelling service site TripIt are only

some of the Semantic Web platform applications. Figure-1.1 and Figure-1.2

summarizes the differences of Web 1.0, Web 2.0, and Web 3.0.

Web 4.0 (a.k.a read-write-concurrency, or the symbiotic web) is the future

generation of the Web. It is still in idea level. It aims creating human-

machine interaction. It will be possible to build more powerful interfaces such

as mind-controlled interfaces with web 4.0[30, 95, 47].


Figure 1.1: Comparisons of Web 1.0, Web 2.0 and Web 3.0 [30]


Figure 1.2: Comparisons of Web 1.0, Web 2.0 and Web 3.0 [95]

Chapter 2

SEMANTIC WEB

The World Wide Web was initially designed to create a universal environment

for document sharing. Over the years main purpose of the internet has shifted

from document sharing to information retrieval. Search engines have become

irreplaceable part of our daily life. As a result, information presented on

web pages were mainly designed in a way that it makes it easier for human

consumption. However, accessing the correct information in such a rapidly

growing environment within a reasonable amount of time is getting harder

and harder. We can use analogy of trying to find a needle in a haystack to

explain looking for information in Web environment.

Semantic Web was first introduced by Tim Berners Lee in 2001. As

Berners Lee stated in [19], Semantic Web is not a separate Web; but it is the

extension of the current web. Semantic Web (a.k.a Web3.0) is designed for

both human and machine consumption. In other words, Semantic Web aims

applying machine processable layer on top of the human processable version.

Although HTML tags are used to create web pages in current Web, those

11

CHAPTER 2. SEMANTIC WEB 12

tags do contain any information about the structure but only focus on the

presentation[80]. This makes current keyword-based search engines sensitive

to vocabulary. Documents that use different terminology than the key words

are often not seen in the search results. In addition, search results not

only returns relevant answers but also returns mildly relevant or completely

irrelevant documents as well. Ratio of correct information becomes too small

compared to total results. Also, current search engines are not capable of

giving an answer to a question but it returns location of a single document

that contains the keywords[4].

By having Semantic Web layer, search engines will not only return the

location of the documents but they will also be able to manage question

answering. Knowledge will be extracted from the web and it will be shown in

a user-friendly mode. In addition, knowledge will be organized according to

its meaning.

Figure 2.1: Semantic Web Layer Cake [4]


Semantic Web has a layered structure consists of multiple steps. Each

step builds another layer on top of previous ones. Semantic Web is based on

hierarchy of languages, each extends the features and capabilities of previous

layers [52]. Figure-2.1 shows the layered Semantic Web architecture[4] defined

by Tim Berners Lee. Due to its layered structure, it is known as Semantic Web

Cake, Semantic Web Layer Cake, or Semantic Web Stack. Due to debates

about this classical layer stack, there are alternative Semantic Web Stacks as

seen in Figure-2.2.

Figure 2.2: Semantic Web Layer Cake [4]

Unicode and Uniform Resource Identifier(URI) are placed in the bottom

layer of the cake. Unicode is a standardized encoding for the character settings

for the Semantic Web. Every resource on the Web has a unique identifier just

like every citizens of countries. URIs are identifiers for the resources on the

Web. For instance, URLs can be given as example of URIs. URLs are subset

of URIs. URLs not only identify a resource but also locate the resources on

the Web[70].

Most of the web pages are designed with Hyper Text Markup Lan-

guage(HTML). HTML provides human-friendly means of representing docu-

ments on the Web. HTML documents are human-centered and designed for

human consumption. Thus, documents presented in HTML are difficult for

the machines to process.

Structure of a HTML document consists of tags. Tags are building blocks

of the language. Most of the tags have to be in the form of open and close

tag pairs. However, there are exceptions such as , <hr>, etc. These

tags do not have to be closed as or </hr>.

<h2>

Nonmonotonic Reasoning : Context−Dependent Reasoning

</h2>

by V. Marekand M. Truszczynski 

 Spr inger 1993

 ISBN 0387976892

Since HTML is not a machine-friendly language, it does not appear on

the Semantic Web Layer Cake as a layer. The partial code written in HTML

above can also be expressed in Extensible Markup Language(XML) as the

follows:

<book>

<t i t l e >

Nonmonotonic Reasoning : Context−Dependent Reasoning

</ t i t l e >

<author>V. Marek</author>

<author>M. Truszczynski </author>

<publ i she r>Spr inger </pub l i she r>

<year >1993</year>

<ISBN>0387976892</ISBN>

</book>

Both of the codes are easily readable by human. However, XML structure

is a lot easier for machines to process because XML files have the structured

information. For instance, for the machines it is difficult to interpret that

Nonmonotonic Reasoning: Context-Dependent Reasoning is a book title and

the book has two authors; however, it is a lot more easier for a machine to

infer that information from the same data written in XML format due to

nested tag structure. XML is a metalanguage for markup. It does not have

predefined tags. It allows users to define their own tags. XML is another

standardized layer in Semantic Web Architecture as seen in Figure-2.1 and

Figure-2.2[4].

Besides XML, there is also XML namespace(NS) and xmlschema in the

second layer of Semantic Web Stack. If two of the applications want to

communicate, all the element and attribute names must be uniquely defined.

Imagine two applications using customer information and product information.


Using the same child element id for both customer and product creates

ambiguity. Thus, id element for both applications should be defined in

different namespaces. XML namespaces are used to uniquely define named

elements and attributes in an XML document. In addition to namespace,

the structure of the XML document should also be defined. XML schema

defines what values an attribute may take, which elements occur within other

elements, which elements might occur or must occur, and so on.

Although XML carries information about structure of the document,

provides tools such as parsers, and provides a means of exchanging data

between applications, it does not give information about the meaning of the

document.

Resource Description Framework(RDF) is another W3C recommendation

to standardize the definition and use of metadata descriptions of Web-based

resources [34]. Everything can be a resource such as books, authors, images,

abstract concepts, relations, etc. RDF consists of subject(S)-predicate(P)-

Object(O) triples. Some resources refers those triples as object-attribute-value

triple as well. RDF triples can be expressed as logical formula P(S,O) such

that binary predicate P relates subject S and object O [80, 4, 72, 112, 84].

An RDF-based model can be represented in a variety of syntaxes:RDF/XML,

N3, Turtle, and RDFa, etc.

RDF statements can be modeled as directed, labelled graphs where nodes

are subjects/objects and labelled arcs are predicates. More complex state-

ments can be constituted by merging simple statements. URIs play curucial

role in RDF. For instance, while creating more complex relations by merging

the graphs based on common nodes, URIs are the only way of making sure

that merged nodes are exactly the same nodes[2].

Figure 2.3: A simple RDF graph representation [34]

Figure-2.3 shows a simple graphical representation for RDF. Turtle repre-

sentation for the same graph is as follows [34]:

@prefix s:<http://www.w3.org/employee/>

<http://www.w3.org/employee/id1321>

<s:hasName>

<“Jim Lerners”>.

<http://www.w3.org/employee/id1321>

<s:authorOf>

<http://www.books.org/ISBN0012515866> .

<http://www.books.org/ISBN0012515866>

<s:hasPrice>

<“$62”>.

Another representation for RDF is RDF/XML language. Figure-2.4 is

Figure 2.4: A simple RDF graph representation [31]

graphical representation of following RDF/XML description:

<?xml ve r s i on="1.0"?>

<rd f :RDF xmlns : rd f="http ://www.w3 . org /TR/ rdf−sytax−grammer/"

xmlns : dc="http :// pur l . org /dc/ e lements /1 .1/"

xmlns : ex="http :// example . org / terms/">

<rd f : De sc r ip t i on rd f : about="http ://www.w3 . org /TR/ rdf−syntax−grammar"

dc : t i t l e ="RDF1. 1 XML Syntax">

<ex : ed i to r>

<rd f : Desc r ip t i on ex : fullName="Dave Beckett">

<ex : homePage rd f : r e s ou r c e="http :// pur l . org /net / dajobe /" />

</rd f : Descr ipt ion>

</ex : ed i to r>

</rd f : Descr ipt ion>

</rd f :RDF>

RDF Schema(RDFS) is a language that provides vocabulary used in

RDF data models. RDF Schema is based on RDF. It allows organizing web

objects into hierarchies such as classes, subclasses, properties, doman/range

restrictions. It can be considered as an ontology language but it is very

primitive. In semantic web a more developed language is needed to represent

more complex relationships between objects [4, 2].

rdfs:Resource, rdfs:Class,rdfs:Literal,rdf:Property, and rdf:Statement are

core classes, rdf:type,rdfs:subClassOf, rdfs:subPropertyOf are the core proper-

ties for defining relationships, rdfs:domain,rdfs:range are core properties for

restricting properties, rdf:subject, rdf:predicate, rdf:object are core properties

for reification, rdf:Bag, rdf:Seq, rdf:Alt, rdfs:Container are container classes,

rdfs:seeAlso , rdfs:isDefinedBy are utility properties in RDFS. Fig-2.5 is an

example of motor vehicles[4].

Figure 2.5: Class hierarchy for the motor vehicles [4]

<rd f :RDF

xmlns : rd f="http ://www.w3 . org /1999/02/22− rdf−syntax−ns#"

xmlns : r d f s="http ://www.w3 . org /2000/01/ rdf−schema#">

<rd f s : Class rd f : ID="motorVehic le"/>

<rd f s : Class rd f : ID="van">

<rd f s : subClassOf rd f : r e s ou r c e="#motorVehic le"/>

</rd f s : Class>

<rd f s : Class rd f : ID="truck">


</rd f s : Class>

<rd f s : Class rd f : ID="pas s enge rVeh i c l e">


</rd f s : Class>

<rd f s : Class rd f : ID="miniVan">

<rd f s : subClassOf rd f : r e s ou r c e="#pas senge rVeh i c l e "/>

<rd f s : subClassOf rd f : r e s ou r c e="#van"/>

</rd f s : Class>

</rd f :RDF>

Listing 2.1: A simple ontology for motor vehicles.

RDF data can be queried. SPARQL Protocol and RDF Query Lan-

guage(SPARQL) is SQL like query language that is executed on RDF for-

matted data.RDF data is stored in a database called RDF Store. RDF stores

can be considered as SQL relational database consists of subject-predicate-

object triples[84, 4, 2].

Figure-2.6 shows a simple RDF graph consists of following RDF triples:


JamesDean

Giant

EastOfEden

RebelWithoutCause

playedIn

playedIn

playedIn

Figure 2.6: A simple RDF relation [2]

:JamesDean :playedIn :Giant

:JamesDean :playedIn :EastOfEden

:JamesDean :playedIn :RebelWithoutCause

Assume RDF database consists of above triples. Let us execute following

SPARQL queries on the database:

SELECT ?who WHERE{?who :playedIn :Giant.}

In this simple SPARQL query above SELECT and WHERE are the

keywords, literals starting with question mark are variables. Thus, “?who” is

a variable in the query. WHERE part of the query is the pattern that will

be seek in the subject-predicate-object database. Predicate and object are

already given in the query. Database will be searched for matching patterns

where predicate is “playedIn” and object is “Giant”. When a matching pattern

found in database, subject of the triples will be returned as a result of the

query. Hence, the answer for the query above will be “JamesDean”.


SELECT ?what WHERE{:JamesDean :playedIn ?what}

Similarly for the query above, the database will be seek for the match-

ing patterns where subject is “JamesDean” and the predicate is “playedIn”.

Database consists of three matching patterns for JamesDean as subject and

playedIn as predicate. “Giant, EastOfEden, RebelWithoutCause” will be

returned as an answer to the query.

Ontology is the representation of terms and their interrelationships. Web

Ontology Language(OWL) is the ontology language of the Semantic Web. It

provides standard vocabulary[95] for machine processable Web. XML, RDF

and RDF(S) are not enough to perform reasoning. OWL is more expressive

than the data created by XML, RDF and RDF(S)[74, 45]. OWL extends

RDF for describing properties and classes: such as disjointness, cardinality,

equality, symmetry, transitivity, inverse of properties, enumerated classes,

etc. Figure-2.7 shows OWL2 structure that is extension and revision of the

OWL[44]. There are three flavours of OWL available : OWL Lite, OWL DL,

OWL Full.

Rules RIF/SWRL enables us to write rules beyond RDFS and OWL[95].

Logic ,Proof, and Trust layers are used for validation of trustability of

inputs. Digital signatures are used to verify origin of the sources for input

data. Trust layer will be created by validation of trusted agents through

digital signatures, certifications and other kinds of knowledge. [4]


Figure 2.7: OWL2 Structure [44]

Chapter 3

KNOWLEDGE REPRESENTATION

3.1 KNOWLEDGE

Definition of knowledge has been discussed for years by philosophers

since ancient Greek times, and still not reached a concrete conclusion. An

informal description of knowledge can be stated as a relation between a

knower and the known [24]. When we say “Pablo knows that some apples

are green”, we define a relation between the knower Pablo and the statement

“Some apples are green”.

Zagzebski [54] defines knowledge as a state of a person’s being in cognitive

contact with reality. Knowledge is a relation between a conscious subject,

and a portion of reality that is knower is related. Knowledge of things can be

direct or indirect. The former one is called as knowledge by acquaintance that

subject gains the knowledge by experience. Knowing Roger as a person can

be an example to knowledge by acquaintance. On the other hand later one is

called propositional knowledge where the subject knows a true proposition

24

CHAPTER 3. KNOWLEDGE REPRESENTATION 25

about the world. Knowing that Roger is a philosopher can be given as an

example of propositional knowledge.[54]

In philosophy propositional knowledge has been discussed more than

knowledge by acquaintance. One of the reasons is that reality becomes

understandable to the human mind when it is stated in propositional form.

Another reason is that knowledge by acquaintance cannot be transferred from

one person to another where as propositions are the form in which knowledge

is communicated.

According to Kumar [63] data is raw form of observations. And knowledge

is organized form of data and procedures that can be used in some other

purposes. When a doctor diagnoses a patient, he/she uses both data and

knowledge to diagnose.

Knowledge can be collected from many sources. Books, movies, the

Internet, pictures, friends, in short everything can be a source for knowl-

edge. Knowledge can be in various types such as declarative knowledge ,

procedural knowledge, heuristic knowledge, meta-knowledge. More

categorizations can also be seen in artificial intelligence such as inherita-

ble knowledge, inferential knowledge, relational knowledge, common sense

knowledge, explicit knowledge, tacit knowledge, and uncertain knowledge.

Declarative knowledge describes facts or assertions. Declarative knowl-

edge includes propositions about “what” is known about the world. Those

propositions are simple statements which can be asserted to be either true or

false. Declarative knowledge can be easily expressed verbally and may change


with new memories. Knowledge can be static or dynamic. Frame structure

can be used to represent static knowledge [104, 63].

“Apple is a fruit.”

The example above gives information about a fact about the world, and

truthness or falseness of the fact can be proven.

Procedural knowledge contains information about “how” to do things.

Knowledge on how to play piano, how to dance, how to bake a cake can be

example for this type of knowledge. This type of knowledge is usually gained

by experience. Procedural knowledge is difficult to express verbally. Most

of the time it requires performing the action to transfer knowledge from one

person to another one. Production rules, condition-action pairs, can be used

to represent procedural knowledge [104, 63].

Heuristic knowledge is also known as shallow knowledge. The knowl-

edge is gained by past experiences in a particular domain. Think of a chess

expert, it is very unlikely that the expert has strong algebraic background or

he/she is expert in mass spectrum analyst. The player uses his prior knowl-

edge and experience while playing the game. This type of “good practice” or

“good guess” can be considered as heuristic knowledge. Knowledge contains

uncertainty in it [63, 36, 55].

Meta-knowledge is knowledge about what we know. In other words,

meta-knowledge is knowledge of other knowledge and knowledge of how to

use other knowledge [105, 43].


3.2 KNOWLEDGE REPRESENTATION FORMALISM

Despite their computational power, many researchers believed computers

cannot learn from scratch. In order to proceed a job that requires intelligence,

a computer should given some information prior to that task. In addition,

information should be stored in the computers so that they become available in

the future [23]. Imagine an intelligent system that is used to diagnose a disease.

The agent cannot diagnose the disease if it has no prior knowledge about

characteristics of the diseases being diagnosed.[73]. The need for representing

and storing information in such form lead researches study Knowledge

Representation (KR) Formalisms.

3.2.1 Roles Of Knowledge Representation

But what is knowledge representation(KR)? Why does it play vital role when

complex systems are built? R. Davis, H. Shrobe, and P. Szolovits describes

knowledge representation in five distinct roles of it [33]:

1. KR is a surrogate.

“A knowledge representation (KR) is most fundamentally a surrogate,

a substitute for the thing itself, used to enable an entity to determine

consequences by thinking rather than acting, i.e., by reasoning about the

world rather than taking action in it.”


KR serves equally well for both tangible and intangible objects. In other

words everything can be represented. However, we have limitations

while representing the real world. A perfect fidelity is nearly impossible

because nothing is the same thing except the thing itself. Therefore, we

cannot represent a thing completely accurate.

While representing the real world, either we omit some of its complex

features or we may add new artifacts that does not exist in the real

world. Having such an imperfect surrogate may cause having incorrect

inferences about the world.

2. A KR is a set of ontological commitments.

“It is a set of ontological commitments, i.e., an answer to the ques-

tion: In what terms should I think about the world?”

All representations are imperfect approximation of the real world. We

represent only the part of the world that we are particularly interested

in and we omit the other parts of it. Deciding on what part of the

world we want to represent and how detailed it will be requires having

ontological commitments. Complexity of real world is tremendous. KRs

provide guidance to what and how to see the real world.


3. KR is a fragmentary theory of intelligent reasoning.

“It is a fragmentary theory of intelligent reasoning, expressed in

terms of three components: (i) the representation’s fundamental concep-

tion of intelligent reasoning; (ii) the set of inferences the representation

sanctions; and (iii) the set of inferences it recommends.”

(i) Intelligent reasoning is defined in many fields. According to

mathematical logic, intelligent reasoning is formal mathematical cal-

culations such as deduction. Psychology defines intelligent reasoning

as a characteristic human behaviour. Biology sees reasoning as the

architecture of the machinery that achieves the reasoning. Probability

theory describes intelligent reasoning by adding concept of uncertainty

to logic in terms of obeying the axioms of probability theory. Eco-

nomics adds values and preferences by defining intelligent reasoning

by adherence to the tenets of utility theory. When we apply one of

these point of views for intelligent reasoning, we not only chose the

representation but also select a conception of the fundamental nature of

intelligent reasoning.

(ii) Which inferences are sanctioned? Sanctioned inferences indicates

which conclusions are allowed be constructed. Each representations

defines sanctioned inferences in a different way in terms of their contents

and forms. In formal logic, sound inferences, in which every model for

the axiom set is also model for the conclusion, are sanctioned. Both


rule based systems and frame-based representations defines sanctioned

inferences based on behaviour of human expert instead of an abstract

formal model. In these representations, conclusions may not always be

sound or true.

iii) Which inferences are recommended? The set of sanctioned inferences

is too large. Hence we should intelligently eliminate those overwhelming

options while reasoning. An automated system should not only consider

sanctioned inferences but also it should consider recommended ones. For

instance from A, we can infer (A∧A) or (A∧A∧A∧A), etc. All of them

sanctioned or legal inferences, however, later ones are not very intelligent

inferences. Representation and reasoning are strongly connected to

each others. While choosing the representation we also point out

how we should inference intelligently. However, formal logic does not

eliminate any sanctioned inference in order to protect its generality and

declarativity. Elimination of any subset of the sanctioned inferences

might be suitable for one situation but not in any other situation

that causes loss of generality. In addition, if language consists of such

statements that declare facts, they cannot not contain any indication of

how to reason with it because by embedding such information they lose

their their declarative character. Instead of representation’s seeking for

the recommended inferences, we let user to recommend set of axioms,

theorems and lemmas provided to the system. By doing so, we increase

the efficiency of computation.


4. KR is a medium for pragmatically efficient computation.

“It is a medium for pragmatically efficient computation, i.e., the

computational environment in which thinking is accomplished. One

contribution to this pragmatic efficiency is supplied by the guidance a

representation provides for organizing information so as to facilitate

making the recommended inferences.”

Reasoning is a computational process and representations are used to

demonstrate how to organize information in a way that inferences can be

made. In order to use a representation, it should be suitable for making

computations with it. One of the goals of representation designers is

finding a way to organize information so that inferences can be made

efficiently.

5. KR is a medium of human expression.

“It is a medium of human expression, i.e., a language in which we

say things about the world.”

We do create representation so that we can describe the world to the

machine or to other people. Hence KR is a means of expression and

communication. KR should be expressive, general and precise so that

communication becomes “easier”.


All of the five roles of KR listed above are crucially important while

designing representation. Ignoring one of them may cause important design

issues. For instance ontological commitment is important when we need

to define how detailed the world be represented. Similarly, the theory of

intelligent reasoning is also important while making inferences. Representa-

tion can guide reasoning once it knows the theory of what reasoning to do.

Pragmatically efficient computation plays an important role too. Most of

the representations are used considering the average case. Creating a weaker

representation in order to improve the worst case performance can misguide

us. The use of a representation as a medium of expression and communication

is also important we should be able to know how to say what we are thinking.

Hence we should be able to know how to use representation, in order to

communicate.


3.3 KNOWLEDGE REPRESENTATION METHODS

3.3.1 NETWORKED REPRESENTATION

3.3.1.1 SEMANTIC NETWORKS

Semantic Networks(or semantic nets) were first used to define concept types

and patterns of relations for machine translation systems[100]. It is then

developed by Ross Quillian in 1966 [26, 87]. Using a model to represent a

context that is expressed in natural language in written format, helps to

identify relationships between instances of the concepts described in the text.

Using such model makes relationships explicit where it is implicit in the text.

Semantic network is a structured knowledge representation method that

consists of interconnected nodes and arcs between these nodes. It was invented

and used in philosophy, psychology, and linguistics before it became a research

field in Artificial Intelligence [98, 99, 13].

Syntax, semantics, and inference rules are three main components of

semantic networks. Syntax consists of specifications about node and arc types.

Semantic is the meaning that is represented by nodes and arcs. Inference

rules are the rules that are used for reasoning [13].

Nodes are used to represent concepts of entities, attributes, events or states

that are objects, abstract form of ideas, knowledge or thoughts. Arcs(links)

are used to represent the relationship between the concept nodes. Links are

directed and labelled. Hence, semantic networks are directed graphs and


labels indicate the relation types. [98, 61].

Figure 3.1: A Semantic Network[6]

There two types of edges: property edges and is-a edges. Property edges

specify properties of objects or concepts and is-a edges indicates hierarchical

relationships. Properties are inherited through is-a edges. For instance,

Kermit inherits its green color from Frog class[6].

Definitional networks, assertional networks, implicational networks, exe-

cutable networks, learning networks, and hybrid networks are the major types

of semantic networks[100].

Definitional networks are the oldest network type among others. It was

first introduced by the Greek philosopher Porphyry in the 3rd century AD. It

indicates is-a relation between a concept and sub-concept. Definitions are

accepted as true by definition. Thus, the information in definitional networks


is assumed to be necessarily true.

Figure 3.2: Tree of Porphyry, as it was drawn by the logician Peter ofSpain(1329) [100]

Figure-3.2 is a version of a the graph drawn by Greek Philosopher Porphyry

as an illustration of Aristotle’s method of defining categories by specifying

the general type and the sub-types of the same super-type. This graph is an

example of definitional networks.

Assertional Networks are used to assert propositions. The information

in an assertional network is assumed to be contingently true. There is various

syntactic versions of assertional networks. Figure-3.3 is a conceptual graph

by Sowa that represents “Sue thinks that Bob believes that a dog is eating a

bone”.

Primary relations in Implicational Networks are implications. Each


Figure 3.3: An assertional network-Propositions represented in SNePS [100]

Figure 3.4: An implicational network [100]

node is a proposition. Directed arcs are implications from one proposition to

another. Figure-3.4 shows possible reasons of slippery grass. The arc labelled

with “T” implies that it recently rained if it is rainy season, otherwise; arc

labelled with “F” implies that sprinklers are in use. Either case implies that

grass is wet, and this implies that grass is slippery.


Executable Networks has three mechanisms: message passing, attached

procedures, graph transformation that can change the network itself. Message

passing mechanism passes a message or token from one node to another,

attached procedures are programs in nodes that executes the data at that

node or nearby nodes, graph transformation breaks graph into smaller graphs,

modifies the graph, or merges graphs. Figure-3.5 has active(diamond) and

passive(rectangular) nodes. Passive nodes can be input and output nodes.

Input nodes takes the input, and active node does calculation on the data

that is sent by passive nodes, and passes it to the output nodes. X =

(A+B)∗S2N(C) can be represented by Figure-3.5, where A,B,C are numbers

and S2N is a procedure that takes a string and converts it into a numerical

value.

Figure 3.5: Dataflow Graphs - An executable network [100]

Learning Networks are constructed from nodes and arcs to represent

knowledge that is retrieved from examples. When new information is intro-

duced, network responds to it and modifies itself so that it represents the new

environment modified by the new information. Network modification can be


Figure 3.6: Learning Networks - Neural Network [100]

done by adding nodes, deleting nodes, or changing the weights on the arcs.

Figure-3.6 shows an example to learning networks. Neural nets are one of the

examples of learning networks. Node addition and deletion is not common in

neural networks. The only network modification can be seen in the weights

of the arcs.

Hybrid Networks are combination of the previously introduced networks.

Most of the complex systems are hybrids. For instance, C++ has an executable

component to provide procedural structure and a definitional component to

define types or classes[100].


3.3.1.2 CONCEPTUAL GRAPHS

Although most semantic networks can be used for question answering and

machine translation, they cannot represent all features of logic. Conceptual

Graph(CG) [96] is knowledge representation formalism that is graphical repre-

sentation of logic based on combination of semantic networks and existential

graphs by Charles Sanders Peirce. It was first introduced by John F. Sowa to

represent the conceptual schemas used in database systems in 1976. Different

expressive power can be obtained by using different subsets of conceptual

graphs. ISO standard conceptual graphs(Conceptual Graph Interchange For-

mat(CGIF)) express the full semantics of Common Logic (CL) and it consists

of subset used for Semantic Web languages[97]. Besides CGIF, there are two

more dialects that are expressing the full CL semantics : the Common Logic

Interchange Format (CLIF), and the XML-based notation for CL (XCL).

Figure 3.7: A Conceptual Graph [97]

Figure-3.7 is a Conceptual Graph represents “On Fridays, Bob drives his


Chevy to St. Louis.” In the graph, rectangles are conceptual nodes, circles

are conceptual relation nodes, the arcs pointing in a circle and pointing

out from a circle are the arguments of that conceptual relation node. Labels in

concept nodes indicates type of the entities for that concept. ∀ in Friday : ∀,

and names such as Bob in Person:Bob, and “St. Louis” in City:“St. Louis” are

the restrictions on the concepts Friday, Person, City respectively. Concepts

without name or universal quantifier are implicitly quantized with existential

quantifier.

Labels on conceptual relation nodes indicates the type of the relation.

Those are agent (Agnt), point-in-time (PTim), destination (Dest), possession

(Poss), theme (Thme), and attribute (Attr).

Graph can be translated in to typed version of predicate calculus as

follows:

(∀x1:Friday)(∃x2:Drive)(∃x3:Chevy)(∃x4:Old) (Person(Bob) ∧ City("St.

Louis") ∧ PTim(x2,X1) ∧ Agnt(x2,Bob) ∧ Poss(Bob,x3) ∧ Thme(x2,x3) ∧

Attr(x3,x4) ∧ Dest(x2,"St. Louis"))

CGIF representation of “On Fridays, Bob drives his Chevy to St. Louis.”

has different syntax than predicate calculus. Square brackets are used to

represent the conceptual nodes, parenthesis is used to represent relation nodes.

Names(e.g. Bob and “St.Louis”, and coreferences(e.g. defining label(*x),

bound label(?x)) are used to create connections between concept nodes and

relation nodes. Univeral quantifier is represented by ASCII string “@every”.

Since graph implies conjunction, ∧ symbol is omitted.


[Person Bob] [Chevy ∗ x1] [Old ∗ x2] (Poss Bob ?x1) (Attr ?x1 ?x2)

[[Friday @every ∗ x3] [Drive ∗ x4] [City ”St.Louis”] (PTim ?x4 ?x3)

(Agnt ?x4 Bob) (Thme ?x4 ?x1) (Dest ?x2 ”St.Louis”)]

Figure 3.8: A Conceptual Graph Representing CL Functions [97]

Figure-3.8 is representation of algebraic formula y = (x+ 7)/sqrt(7). In

the figure, conceptual relations(functions) are represented by diamond-shaped

nodes, that are called actors. Empty nodes represents result of actors Add

and Sqrt. Arcs labelled with numbers 1 and 2 are used to indicate the order in

which the arcs are written in CGIF. CGIF representation of y = (x+7)/sqrt(7)

is as follows:

[Number : ∗x] [Number : ∗y] [Number : 7] (Add ?x 7 | [∗u])

(Sqrt 7 | [∗v]) (Divide ?u ?v | ?y)

In the CGIF statement above, input nodes are separated from output

nodes by a bar (|).


3.3.2 STRUCTURAL REPRESENTATION

3.3.2.1 FRAMES

Frames were proposed by Marvin Minsky in 1974[76]. A frame is a data

structure used to create structured knowledge representation for stereotyped

knowledge such as a visual scene like being in a certain type of a living-

room, or an event like going to a child’s birthday, or a complex structure like

automobile parts. Frames are inspired from human understanding. They are

model of human memory and cognition. When someone encounters a new

information about previously known problem, our brain brings a particular

memory frame from our memory and it gets updated with the new information.

A frame can contain information about how to use the frame itself, what to

expect next, or what to do when expectations are not met. Collection of

similar frames, that are linked together generates frame-systems.[76]

A frame provides a structured representation of an object or a cate-

gory(class). An object such as Paris is represented by individual frames. A

category such as European Capitals is represented by generic frames. Class

taxonomies are achieved by using constructors. Constructors enables to draw

sub/super-class relation between classes. A frame can contain attributes of

an object or a category, and their relations to other objects or categories.[39,

76]

Frames resembles records in terms of structural knowledge. Unlike records

frames have slots and fillers instead of field names and values in records. In

Figure 3.9: Comparison of OOP, Frames, DLs and RDF[65]

addition, frames are related to semantic networks, which is also predecessor

of early description logics language KL-ONE. Frames and object oriented

languages(OOP) are also similar except the terminology used in both. Figure-

3.9 shows the comparison of OOP, Frames, Description Logics and RDF[65].

(frame-name

<slot-name1 filler1>

<slot-name2 filler2 >

...

)

The template above is the general form for a frame. Each frame has a

name representing an object or a class of objects. Slots are attribute descrip-

tions for a class or an object. Knowledge Engineering Environment(KEE)

system[65] provides two different types of slots: ownslots and memberslots.

Ownslots consist attributes of the object or the class that is represented

by the frame itself. Memberslots resembles database schema. They draw a

general description for each member of the class rather than having attribute

description for the class that is represented by the frame itself.


Figure-3.10 presents class taxonomy for the transportation in knowledge

base. Solid lines indicate class-subclass relations and dashed lines indicate

class-membership relations. For instance, MEN is subclass of PEOPLE and

PAUL, and FRED are members of class MEN. Both solid and dashed lines

indicates “IS-A” relation either between an instance and a class, or a class

and its super class.

Figure-3.11 is a frame for generalized class AUTOMOBILES and Figure-

3.12 is a frame for CAR2, which is a specific instance of AUTOMOBILES

class. Cardinality.Min and Cardinality.Max facets are the constraints for the

fillers of the slots. ValueClass facet describes which class the slot belongs to.

Sub-classes inherit properties from their super-classes.

Figure 3.10: The Transportation Knowledge Base[39]


Historically, there are two aspects for frame semantics. The first one is AI

aspect introduced by Minsky, which is described above and are considered

as cognitive frames. That is the general form of the frames. Cognitive

frames, slot-filler representations,a data-structure representing a stereotyped

situation, play an important role in how people perceive, remember, and reason

about their experiences. Minsky’s frames are highly structured knowledge

representation approach, which collects information about particular objects

and events and arranges them into a taxonomic hierarchy. On the other hand,

the second approach has linguistic aspect introduced by Fillmore. Fillmore’s

frames characterizes an abstract scene which identifies the participants of

the scene and sentences describing the scene. According to Fillmore, one

cannot understand the meaning of a single word without access to all the

essential knowledge that relates to that word. Understanding a sentence of

the language requires having mental access to such schematized scenes.[42,

48]

We would like to clarify, FrameNet Project[12] explained in Chapter-4

refers Fillmore’s definition of frames, mostly referred as semantic frames.

From this point on, the word “frame” will refer semantic frame.

According to Fillmore, one word evokes or activates the whole scene (a

frame) related to that word. The examples below shows how the wording

changes our perception about the same event.

(1) I spent three hours on land this afternoon.

(2) I spent three hours on the ground this afternoon.

Two of the scenes above invokes different scenes[41]. The first one invokes


a scene about a sea voyage, and the second scene invokes an interruption of

an air travel each of which are different frames.

Another famous example of frame semantic is Commercial Transaction

Frame that consists frame elements(FE) such as buyer, a seller, goods, and

money. Each of these words, focuses on different aspects of the frame but

still related to each others. For instance, “buy” focuses on the “buyer” and

“goods”; “sell” focuses on the “seller” and “goods”, etc. The idea is one would

not be able to understand the word “sell” without knowing anything about

the situation of Commercial Transaction.[83, 48]


3.3.2.2 KL-ONE KNOWLEDGE REPRESENTATION SYSTEMS

KL-ONE (also known as KLONE) is a well-known knowledge representation

formalism in Artificial Intelligence that is introduced by Brachman in his

Ph.D thesis [111, 22]. KL-ONE is descendent of semantic nets and frames.

It is introduced to overcome ambiguity and inconsistency of semantic nets

and frames. Brachman wanted to create a knowledge representation struc-

ture that is strictly dependent on logic, that is more knowledge structuring

level, in his words “epistemological”, than application-based or real world

representation-based representations[7]. Development of KL-ONE later leads

to development of description logics(DLs). KL-ONE systems has been used

in many applications in Artificial Intelligence such as understanding and gen-

erating natural language, information retrieval, natural language command

execution, and many others [25].

KL-ONE consists of two parts that are descriptions and assertions. De-

scription part allows us to describe simple and compound terms. For instance,

“a man from Betelgeuse” is a compound term that uses the description of

man and Betelgeuse. Description part consists of two sub-parts: primitive

and defined. Primitives are not fully described with all properties. They are

considered as incomplete definitions. On the other hand, defined descriptions

are characterized by all the necessary and sufficient conditions. For instance,

a polygon can be defined as a primitive with the property of having three or

more line segments. We do not attempt to list all properties of primitives.

A defined concept triangle can be derived from the polygon’s description.

A triangle is a polygon, that has three sides that are line segments. This

definition gives all necessary and sufficient conditions for being a triangle.


Thus, triangle is a defined concept. However, based on the given definition of

a polygon, it does not guarantee a geometric shape, that has three or more

line segments to be a polygon if there are edges, that are not closed. Assertion

part allows us to do reasoning on descriptions. Just like DLs, KL-ONE

consists of notion of concepts, roles, and their relations, number restrictions,

class hierarchies, and classifications.[25]

Figure 3.13: Truck and TrailerTruck concepts defined in KL-ONE [101]

The figure-3.13 is a simple KL-one graph. Ellipses are defined concepts,

ellipses with shades are individual concepts, ellipses with asterisk are primitive

concepts. Roles are denoted with circles in the middle of arrows. The v/r

notation indicates value restrictions or type constraints for those roles. Large

arrows indicate class subsumption relation.

Graph can be written as frame-like syntax as follows[101]:

“Every truck is a vehicle.

Every trailer truck is a truck that has

as part a trailer,

an unloaded weight, which is a weight measure,

a maximum gross weight, which is a weight measure,

a cargo capacity, which is a volume measure,

and a number of wheels, which is the integer 18.”

Syntax(α) Semantics(〚α〛)

c 〚c〛= µ(c) ⊆ δ

r 〚r〛= µ(r) ⊆ δ × δ

(and c1...cn) 〚(and c1...cn)〛= 〚c1 〛∩...∩ 〚cn 〛

(exists r) 〚(exists r) 〛= {x ∈ δ | ∃y ∈ δ such that <x,y> ∈ 〚r〛}

(all r c) 〚(all r c) 〛= {x ∈ δ | ∀y ∈ δ, if <x,y> ∈ 〚r〛then y ∈ 〚c 〛}

(= r1 r2) 〚(= r1 r2)〛= {x ∈ δ | ∀y ∈ δ, <x,y> ∈ 〚r1〛just in case <x,y> ∈ 〚r2〛}

(vrdiff r c) 〚(vrdiff r c)〛= {<x,y> ∈ 〚r〛 | y ∈ 〚c〛}

(chain r1...rn)〚(chain r1...rn)〛= {<x,y> ∈ δ × δ | ∃z1...zn−1 such that

<x,z1> ∈ 〚r1〛...<zn−1,y> ∈ 〚rn〛}

Figure 3.14: Common type-forming operators[109]

The principle component of KL-ONE systems is the concept and main

relation between concepts are the subsumption[90]. Concept A subsumes

concept B if every instance of B is also an instance of A. In that case, concept

B inherits all attributes from concept A. KL-ONE uses structured inheritance

networks to draw such relations between concepts[111].


Figure-3.14 summarizes syntax and semantics of concept- and role forming

expressions with respect to a domain δ and a modeling function µ. µ assigns

interpretations in δ to atomic concepts and roles. µ(c) ⊆ δ and µ(r) ⊆ δ × δ

holds for every atomic concept and role respectively. Atomic concepts are

denoted by c, and atomic roles are denoted by r in the first two lines of

the table. Concepts and roles after the first two lines can be atomic or

complex[109].

Although, KL-ONE is used in wide range of fields, many studies showed

that even for simple languages, subsumption is intractable or undecidable[109].

Schmidt-Schauß[91] proved that subsumption relation is undecidable even

when language only consists of =, and, all, and chain.


3.3.3 LOGIC-BASED REPRESENTATION

There are various types of logic such as propositional logic, predicate logic(or

first order logic), temporal logic, fuzzy logic, description logic, F-logic etc.

Here we will be focusing on propositional logic, first order logic, F-logic, and

description logic. We will go into more detail in description logic part since it

is standardized layer in semantic web.

Language Ontological Commitment Epistemological CommitmentPropositional Logic facts true/false/unknownDescription Logic facts, objects, relations true/false/unknownFirst-Order Logic facts, objects, relations true/false/unknownTemporal Logic facts, objects, relations, time true/false/unknown

Probability theory facts degree of belief ∈ [0,1]Fuzzy Logic facts with degree of truth known interval value

Figure 3.15: Formal Languages Ontological And Epistemological Commit-ments[89]

Figure-3.15 shows ontological and epistemological commitments of different

logical languages. Propositional logic consist of facts, which can be true, false

or unknown. First-order logic(FOL) consists of facts, objects, and relations

which can be true, false, or unknown. Since description logic is a decidable

fragment of FOL, it has the same ontological and epistemological commitments

as FOL. Ontological commitment of temporal logic consists of time values in

addition to facts, objects and relations that can be true, false, or unknown.

Probability theory consists of facts, that has degree of belief in [0,1] interval.

Fuzzy logic is set of facts with degree of truth for some known interval value.


3.3.3.1 PROPOSITIONAL LOGIC(PL)

A proposition is a statement, that can be evaluated as true or false. Proposi-

tional logic(sentential logic,sentential calculus, statement logic) is a branch of

logic, that studies means of combining propositions to create more complex

propositions or means of altering the propositions[60].

The simplest preposition is an atom denoted by capital letters such as P,

R, Q. “Today is Monday.” can be an example to an atom. An atom can be

either true or false. More complex prepositions can be created from atom by

using AND(∧), OR(∨), NOT(¬), implication(→), and iff(↔) connectives[82].

A logical formula can be define recursively as follows:

• Every atom is a formula.

• If φ, ψ are formulae, then ¬φ, φ ∧ ψ, φ ∨ ψ, φ → ψ, and φ ↔ ψ are

formulae.

A formula is called a well-formed formula(wff) if is syntactically correct.

A well-formed formula can be described as follows[81]:

wff ::= atomic proposition | (wff)| true | false | ¬ wff | wff ∧ wff |

wff ∨ wff | wff → wff | wff ↔ wff

Figure-3.16 shows formal definitions of the connectives. NOT(¬) flips

the truth value of a statement. AND(∧) outputs true if both prepositions

are true. OR(∨) outputs true iff at least one of the propositions are true.

Implication(→) yields false only when φ is true and ψ is false. Equality(↔)

outputs true if both sides of the arrow carry the same truth value.


φ ψ ¬φ φ ∧ ψ φ ∨ ψ φ→ ψ φ↔ ψ

T T F T T T TT F F F T F FF T T F T T FF F T F F T T

Figure 3.16: Truth table of connectives in propositional logic

Truthness of a proposition is determined by interpretation I. Truth table

of a formula φ is mapping from interpretation I to truth value of φ.[82]

• Truth value of an atomic proposition φ is φI in the interpretation I.

• If φ = ¬ψ, then φI = ¬ψI .

• If φ is a complex proposition such as φ = p∧q, then φI = pI ∧qI . Same

rule holds for OR, implication, and iff as well.

Formulae φ and ψ are equivalent, if they have the same truth table. In

other words, φ ≡ ψ if they yield the same truth value for all interpretations

I.

• A wwf φ is satisfiable if there exists a truth assignment I that is

φI = T . We say interpretation I entails φ and we denote it as I |= φ.

• A wwf φ is tautology(or valid), if for all interpretations I, I |= φ.

• A wwf φ is contradiction(or invalid), if for all interpretations I, I 6|= φ.

• A wwf is contingency if it is neither a tautology nor a contradiction.


Logical Inferences in PL:

If every interpretation that entails set of the formulae {φ1, φ2, ..., φn} also

entails φ, then we say φ is a logical consequence of φ. In other words, every

truth assignment I that satisfies {φ1, φ2, ..., φn} also satisfies φ, and denoted

by φ1, φ2, ..., φn |= φ. Entailment holds if and only if (φ1, φ2, ..., φn) → φ is

tautology.[81]

A logical consequence is formally drawn by two different ways: model-

theoretic/semantic consequence(|=) or proof-theoretic/syntactic consequence

(`). Checking validity of an argument with n propositional variable requires

having 2n lines in the truth table when model-theoretic approach is used. As

a result, when the number of the variables increases in a proposition, the

time required for checking the validity increases exponentially and becomes

cumbersome. In that case, using proof-theoretic approach with inference

rules to check the validity of an argument becomes more effective. Inference

rules allow us to infer new formulas by using the given ones. Figure-3.17

summarizes some of the inference rules used in PL.[88, 81]

For instance by knowing ¬C and ¬C → (A→ C) are valid, we can derive

that ¬A is also valid[81]:

1) ¬C (an axiom)

2) ¬C → (A→ C) (an axiom)

3) A→ C (Modus Ponens, from line 1 and 2)

4) ¬A (Modus Tollens, from line 3 and 1)


Figure 3.17: Inference Rules in PL[88]


3.3.3.2 FIRST-ORDER LOGIC(FOL)

First-order logic, also known as first-order predicate calculus or predicate logic,

extends propositional logic by including quantification over the individuals

of the domain of discourse[14]. Basic building blocks of FOL syntax are

symbols for constants to represent objects, predicate symbols to represent

predicates(or relations), and function symbols to represent functions.

Constants in FOL are represented with lower-case letters a, b, c etc. A

predicate has an arity of n, where n ∈ N. Predicates are denoted by capital

letters such as P, Q, R etc. A function has an arity of m, where m ∈ N+.

Functions are denoted by lower-case letters f, g, etc. [89, 103]. Terms refers

to an object and defined by the grammar :

t := c | x | f(t1, t2, ..., tn)

where c ranges over constants, x ranges over variables, f ranges over n-ary

function symbols, and t1, t2, ... , tn over terms, for each integer n ≥ 1.

A well-formed formula can be define as follows:

wff := P (t1, ..., tn) | t1 = t2 | (wff) | True | False | ¬ wff | wff ∧ wff |

wff ∨ wff | wff → wff | ∀x wff | ∃x wff

where P ranges over n-ary relation symbols, t1, t2, ..., tn ranges over term

symbols for n ∈ N, and x ranges over variable symbols.


P (t1, ..., tn), t1 = t2, True, False are atomic formulae (a.k.a atomic

sentences or atoms).

Mother(julia) , MotherOf(Doctor(julia),Student(john))

Two of the sentences above are examples for atomic sentences. First

example indicates “Julia is a mother”. Second example has complex terms

as an argument to represent relation that “Doctor Julia is mother of student

John”.

Complex sentences(complex formulae) are created by using logical

connectors. Logical connectors negation(¬) , conjunction(∧), disjunction(∨),

implication(→) behave same as in PL. Order of logical connectors also repre-

sents their precedence from the highest to the lowest.[89, 103]

Country(france) ∧ Capital(paris) ∧ In(paris, france)→

CapitalOf(paris, france)

The example above is a complex formula representing “Paris is capital

of France.” Terms without variable are called ground term. A variable

in a formula can be bound or free. A free variable is the one that is not

quantified in the formula.

∀xP (x, y)

In the formula above x is a bound variable and P is its scope; variable y

in the same formula is a free variable if x 6= y. A variable is defined free:

• if φ is an atomic formula and if x occurs in φ, then x is free.

• if x is free in φ, then it is free in ¬φ


• if x is free in φ or ψ, then it is free in ψ ∧ φ, ψ ∨ φ, ψ → φ.

• if x is free in φ and x 6= y, then x is free in ∀yφ and ∃yφ.

The De Morgan Law

∀x ¬P ≡ ¬∃x P ¬(P ∨Q) ≡ ¬P ∧ ¬Q

¬∀x P ≡ ∃x ¬P ¬(P ∧Q) ≡ ¬P ∨ ¬Q

∀x P ≡ ¬∃x ¬P P ∧Q ≡ ¬(¬P ∨ ¬Q)

∃x P ≡ ¬∀x ¬P P ∨Q ≡ ¬(¬P ∧ ¬Q)

Unquantized De Morgan’s Law applies to PL predicates as well, where x

is a variable, and P and Q are predicates.

Syntax is only set of symbols for the grammar of the language. Meaning

of the symbols are given by the semantic. Semantics deals with the inter-

pretation of language including meaning, logical implication, and truth[108].

Semantics can be achieved either by proof-theoretic semantics or by Model-

Theoretic semantics. Both are useful methods, however, we will introduce

model-theoretic semantic here since description logic adapts model-theoretic

semantic.

An interpretation or model (I) of a logical formula contains semantics

for constants, predicate symbols, and function symbols. Models in proposi-

tional logic links propositional symbols to truth values. Models in FOL are

different than PL. Domain of the models in FOL are nonempty and consists of

set of objects or domain elements[89]. In PL an interpretation fixes the truth-

ness of a given proposition. For instance, truth value of (P ∨¬Q)→ (Q→ P )

can be evaluated by constructing a truth table for the formula in PL. In


contrast, it is not that simple to follow the same approach for the formula

∀x∃y((P (x) ∨ ¬Q(y))→ (Q(x)→ P (y))) in FOL. Meaning of the quantifiers

and their dependence, and the actual parameters of P and Q should be

reflected as well. In addition to formulas, predicates such as P (t1, t2, ..., tn)

cannot be evaluated by truth assignment without knowing the meaning of

the terms. For example, P could denote “less than or equal to” relation on

terms that are real numbers. Thus, a model is needed to evaluate constant

symbols, predicate symbols and function symbols [53].

In FOL, a model evaluates whether constant, predicate, and function

symbols reflects the objects, relations and functions in the domain of discourse.

Model of a set of function symbols F and a set of predicate symbols P can

be defined as follows:

• A non-empty set 4I ; the universe of concrete values

• for each null-ary function symbol(constant) f ∈ F , a concrete element

fI ∈ 4I .

• for each f ∈ F with arity n > 0, a concrete function fI : (4I)n →4I

• for each P ∈ P with arity n > 0, a subset P I ⊆ (4I)n of an n-place

relation on 4I .

Let I be a model for a variable-free term t, c be a constant symbol and f

be a n-ary function symbol:

• if t = c , then tI = cI

• if t = fI(t1, t2, ..., tn), then tI = f(t1I , t2

I , ..., tnI)


Let I be a model for a predicate symbol P, and t1, t2, ..., tn be variable

free terms:

• if t = P (t1, t2, ..., tn), then tI = P I(t1I , t2

I , ..., tnI)

Truth value of 4I |= (x = 2) depends on the value x holds. We need a

look-up table environment that assigns values to x. An environment α is used

to assign values to the variable. Let α be the value binding function from set

of variables var to domain. α : var →4I denoted by α[x 7→ a], which maps

x to a, where a ∈ 4I .

We replace every variable in α : var → 4I with a term and we define

α′ : term→4I as follows :

• α(x) is identical to α′(x) except that α′(x) = c, where c ∈ 4I ,

• α(f(t1, ..., tn)) = fI(α′(t1), ..., α′(tn)), where n is the arity of f, and

t1, ..., tn are terms,

• if f is null-ary function, then α′(f) = fI .

If I |=α φ holds, then we say that formula φ computes to true in the

model I with respect to the environment α.[53]

• if φ is P (t1, ..., tn), where terms consist variables, then each variable

is replaced by α with their values a1, a2, ..., an ∈ 4I . We say I |=α

P (t1, ..., tn) holds if a1, a2, ..., an ∈ P I .

• The relation I |=α ∀xφ holds iff I |=α[x 7→a] φ holds for all a ∈ 4I .

• The relation I |=α ∃xφ holds iff I |=α[x 7→a] φ holds for some a ∈ 4I .


• The relation I |=α ¬φ holds iff it is not the case that I |=α φ holds.

• The relation I |=α φ ∨ ψ holds iff I |=α φ or I |=α ψ holds.

• The relation I |=α φ ∧ ψ holds iff I |=α φ and I |=α ψ holds.

• The relation I |=α φ → ψ holds iff I |=α ψ holds whenever I |=α φ

holds.

Although FOL is a very expressive language that can express majority

of the natural language, it has been heavily criticized for complexity of

its reasoning algorithms[46]. In the following section, we will introduce a

decidable fragment of first order logic, that is one of the fundamental layers

of semantic web architecture.


3.3.3.3 DESCRIPTION LOGICS

Description Logics(DLs)1 are a family of the knowledge representation for-

malism. DLs are descendent of KL-ONE systems[25] that is used to represent

the knowledge of the domain of the application formally. After early im-

plementation KL-ONE systems, worst case complexity of KL-ONE-like KR

languages became major problem in the field. Complexity of the language has

direct relationship with expressive power of the language. Inference problems

such as subsumptin relation between concepts is intractable, although the

language is not very expressive. Unlike FOL researchers who are mainly

focusing on theorem-proving, DLs researchers focus on query answering in

reasonable time. However, having intractable inferences does not make DLs a

bad candidate as an ontology building language since optimization techniques

and restrictions are used when implementing a system. [7] A logic based

ontology language enables reasoning about the the relationships between

concepts and objects[51].

Basic building blocks of DLs are atomic concepts, atomic roles, and

individuals. Concepts represent sets of individuals in the domain, roles are

binary relations between individuals in the domain, and individuals are single

individuals in the domain. Concepts are like unary predicates, roles are like

binary predicates, and individuals are like constants in FOL[62, 106]. In

addition to atomic concepts and roles, more complex concepts and roles can

be constructed by using constructors that are provided by different languages.

Description languages are identified by the constructors they provide. The

most basic description language is Attributive Language(AL). Concept and1Majority of this section summarizes content and examples from[7, 9, 62, 8, 10].


role descriptions supported by (AL) as follows[7]:

C:= A | > | ⊥ | ¬A | C uD

R:= ∃R.> | ∀R.C

whereA is atomic concept, > is universal(top) concept, ⊥ is bottom(empty)

concept, C and D are concept descriptions,and R is an atomic role. Negation

can only be applied on atomic concept, and existential quantifier is restricted

by only top concept.

More expressive description languages can be obtained by different con-

structors. Each constructor is represented by a letter. Language gets its name

from the constructor it supports such asALC, SHOIN, SHOIN(D), SROIQ,

etc.

There are two kind of semantics for OWL2 : direct semantics, which is

compatible with the description logic SROIQ or RDF-Based semantics[77,

44]. We will introduce SROIQ(D) and its properties in the following parts

of this section.


C U + E

S AL+C + Transitivity of Roles

U Concept Disjunction

E Full Existential Quantification(∃R.C)

H Role Hierarchies

O Nominals

I Inverse Roles

N Number Restrictions (≤ nR)

Q Qualified number restrictions (≤ nR.C)

(D) Data types

F Functional Roles

R Complex Role Inclusion

Table 3.1: Constructors in Family of AL-Languages


SROIQ(D)

DL does not contain entire state of the world. It consists of partial

statements about the world. Those statements are called axioms. Axioms

are logical statements that are evaluated to either true or false. There are

three types of axioms in DLs: assertional axioms(ABox), terminological

axioms(TBox), and relational axioms (RBox)[62].

ABox axioms are statements about named individuals. ABox axioms rep-

resent knowledge about how individuals related to each other(role assertion),

or which concept they belong to(concept assertion). ABox is also refereed as

the world description[7].

Capital(paris), Country(france), CapitalOf(paris,france)

First two ABox axioms above are example for concept assertion indicating

that individual paris belongs to set Capital, and individual france belongs

to set Country. Last axiom is concept assertion indicates the type of binary

relation between individuals paris and france.

tom ≈ thomas , tom 6≈ john

DLs do not support unique name assumption, different individual names

might represent same individual. The example above indicates individual

equality and inequality respectively.


TBox axioms , or the terminology represents the relationship between

concepts. TBox axioms consist concept equality and concept inclusion.

Parent v Ancestor

Parent concept above is subsumed by Ancestor concept. In other words,

every member of Parent concept is also member of Ancestor concept[62].

Subsumption and instance relationship provides implicit semantics of “IS-

A” relation in semantic networks. In semantic networks user explicitly has

to set IS-A relationship, however, in DLs it can be implicitly inferred by

subsumption and instance relationships[7].

Concept1 ≡ Concept2

Class equality is represented by ≡ symbol and it holds when every member

of Concept1 is member of Concept2 and every member of Concept2 in also

member of Concept1 ((Concept1 v Concept2) ∧ (Concept2 v Concept1)).

RBox axioms are used to represent properties of roles such as role inclu-

sion, role equivalence, role composition, and disjoint roles. An example to

role inclusion :

role1 v role2

indicates that every pair of individuals related by Role1 is also related by

role2. parentOf v ancestorOf indicates that if person x is parent of person y,

then person x is also ancestor of person y.


brotherOf ◦ parentOf v uncleOf [62]

Role composition can only appear on the left hand side of complex role

inclusions as seen above. If person x is brother of person y, and person y is

father of person z, then person x is uncle of person z.

Disjoint(motherOf, fatherOf)

There are cases that pair of individuals that appear on a relation, strictly

cannot appear on other relations such as nobody can be both mother and

father of the same individual. Disjoint roles are used to represent such cases.

More complex concepts and roles can be defined by using basic ABox,

TBox, RBox axioms and the constructors. Figure-3.18 has set of axioms that

define family relationships.

Figure 3.18: A terminology(TBox) concepts about family relationships[7]

Top(>) concept is used to represent all individuals in the domain and

bottom(⊥) concept is used to represent an empty concept. > ≡ C t ¬C and


⊥ ≡ C u ¬C where C is an arbitrary concept[62].

DLs allow to use concepts and roles linked together to create restriction on

roles. (∃parentOf.>) u (∀parentOf.Female) axiom represents all individuals

who are parents of at least one child and all of their children are females.

parentOf role is restricted with existential quantifier and top concept.

Person v (≥2childOf.Parent u ≤2childOf.Parent)

The axiom above is an example to number restriction of roles. It represents

set of individuals who have at least and at most two parents (individuals who

have exactly two parents).

Enumerations are not allowed in DLs, however, they can be simulated

by nominals. A nominal is a set that has only one named individual as its

instance.

Weekdays ≡ {monday} t {tuesday} t {wednesday} t {thursday} t {friday}

Sets can be defined without disjunctions by using set(or one-of constructor)

as well. A set constructor defines a set {a1, ..., an} where ai’s are individual

names(i ∈ {1, 2, , ..., N}).

Another constructor is fills constructor(R:a) that defines set of individuals

that are fillers of role R.

hasChild: john


John is role filler of hasChild role. In other words it defines set of

individuals who has a child named John.

Complex roles can be created by using role constructors. Universal role

U is a role that relates every pairs in the domain. An empty role can be

represented as > v ¬∃R.> Every individual is not related through role R.

ancestorOf ◦ ancestorOf v ancestorOf

The axiom above represents that ancestorOf role is transitive. If inverse

of a role equals to role itself, then the role is symmetric. If inverse of a role is

disjoint from itself, then the role is asymmetric.

marriedTo ≡ marriedTo−(symmetric), Disjoint(sonOf,sonOf−)(asymmetric)

Global reflexivity can be represented by combining top concept with local

reflexivity. A role is irreflexive if it is not locally reflexive.

> v ∃knows.Self(reflexive) , > v ¬∃marriedTo.Self(irreflexive)

We can summarize SROIQ(D) description language by giving its formal

syntax[62]. A SROIQ(D) concept C is defined by the grammar below, where

n ∈ Z+, NC is a set of concept names, and NI is a set of individual names:

C := NC | (C u C) | (C t C) | ¬C | > | ⊥ | ∃R.C | ∀R.C | ≥ nR.C | ≤

nR.C | ∃R.Self | {NI}


SROIQ role expressions R is defined by the following grammar where U

is universal role and NR is a set of role names:

R := U | NR | N−R

Table-3.2 is summary for the formal syntax of SROIQ axioms.

ABox : C(NI) , R(NI , NI) , NI ≈ NI , NI 6≈ NI

TBox : C v C , C ≡ C

RBox : R v R , R ≡ R , R ◦R v R , Disjoint(R,R)

Table 3.2: Formal Syntax of Axioms in SROIQ [62]

An ontology consists of set of these axioms listed above. Structural

restrictive rules are applied to the ontology in order to have a terminating

and correct reasoning algorithms[62]. In SROIQ following roles are restricted

with simple roles, where a simple role is a role that does not contain role

composition (e.g. if S ◦ T v R , then R is not simple):

Disjoint(R,R) , ∃R.Self , ≤ nR.C , ≥ nR.C

Besides simplicity restriction, there is regularity restriction. Regularity

restriction limits cyclic dependencies between complex role inclusion axioms.


Figure 3.19: Formal Syntax and Semantics of SROIQ [62]

Description logics are designed to represent domain of interest. Unlike

databases, DLs are not describe complete state of the world. DLs follows

Open World Assumption where unspecified axioms are not strictly false as

oppose to database’s Close World Assumption.

There is no formal relation between syntax and the axioms defining

the domain. Formal semantic of the language is given by model-theoretic

semantic. Formal semantic of DLS depends on interpretation of axioms I.

An interpretation is a pair of interpretation domain 4I and an interpretation

function .I , that assigns to every atomic concept A a set where AI ⊆ 4I and


to every atomic role R a binary relation RI ⊆ 4I ×4I :

I = (4I , .I) .

Figure 3.20: Formal Syntax and Semantics of SROIQ Axioms[62]

Figure-3.19 and Figure-3.20 summarizes formal syntax and semantics of

individuals, concept and role constructors and ABox, TBox, RBox axioms. For

instance, interpretation of CuD in Figure-3.19 is intersection of interpretation

of concept C and interpretation of concept D.

(C uD)I = CI ∩DI

If an ABox, TBox, or Rbox axiom α satisfies the conditions in Figure-

3.20, then we say interpretation I satisfies the axiom α, or α holds in I

(I |= α). I is a model of ontology O, if all axioms in the ontology hold in

I. If an ontology does not have a model then it is called inconsistent, and it

entails every axiom α in it[62, 51]. An inconsistent ontology, cannot provide


meaningful conclusions. Inconsistency might happen during the construction

of the ontology. There are techniques such as “repair and publish” to deal

with such inconsistencies[51]. One of the technique is identifying the smallest

subsets called justification of the ontology that creates the inconsistency and

fixing them.

DLs do not have Unique Name Assumption. Different individuals may be

interpreted as the same individual. In addition, interpretation domain might

consist individuals other than named individuals. Example below looks like

an inconsistent justification[62]:

parentOf(julia, john)

manyChildren(julia)

manyChildren v 3 parentOf.>

Example above describes “having many children” as being parent of at

least 3 individuals. Since Julia has many children and only John is given,

a misinterpretation might argue that this ontology is inconsistent, however;

these type of wrong assumptions can be eliminated by knowing that DLs are

following open world assumption.


3.3.3.4 FRAME LOGIC(F-LOGIC)

F-Logic[71] or Frame logic is a knowledge representation language that com-

bines advantage of object-oriented data model, frame-based languages and

logic-based languages. Declarative languages do not support abstraction and

object identity, and object oriented languages suffer from lack of formal seman-

tics. F-Logic combines features of both languages. It includes classes, complex

objects, methods, inheritance, queries, encapsulations, defining, querying and

manipulating database schema. Development of Semantic Web increased the

need for logic-based languages for processing distributed knowledge on the

Web [58, 3, 57].

Figure 3.21: Part of an IS A Hierarchy [58]


Figure-3.21 indicates is-a hierarchy of classes and objects. In F-Logic

since classes and individuals are defined in the same domain, they can be

manipulated with the same language. Solid arcs indicates class/subclass

hierarchy and dotted arcs indicates class membership. For instance student

and empl classes are subclass of person. And phil is member of empl class.

In F-Logic subclass relationship is denoted by (::) and class membership is

denoted by (:). Some of the relationships can be listed as follows:

empl :: person

student :: person

child(person) :: person

sally : student

integer : datatype

. . .

Figure-3.22 is a simple ontology-based application[3]. Ontology consists

of class hierarchy, rules, facts and queries. Figure-3.22 states that every

individual in man and woman objects are person. In the figure person object

has four attributes: father, mother, daughter, and son. A person has 0 or 1

father who is a man. Similarly a person has 0 or 1 mother who is a woman.

Attributes may have range. For instance, person[daughter∗=>woman]

limits the range of daughter by woman.

Object names and variable names(id-terms), are the basic syntactic el-

ements of F-Logic. Variables such as ?X, ?Y, ?Z in F-Logic are indicated

with prefix “?” in order to be able separate them from object names. Second


Figure 3.22: A simple ontology [3]

part of Figure-3.22 shows set of rules defined for the ontology. Rules consist

two part head and body demonstrated as head:-body. The head of the rule

is an F-molecule and the body is a Boolean combination of F-molecules or

negated F-molecules.

?X[ancestor -> ?Y] :- ?X[parent -> ?Y].

?X[ancestor -> ?Y] :- ?X[ancestor -> ?Z], ?Z[parent -> ?Y].

F-Logic allows having recursive rules as given the example above to define

ancestor relationship. If someone has a parent, then that person has an


ancestor. In addition, if person X has an ancestor Z and person Z ancestor

has a parent Y, then person Y is also ancestor of person X.

Variables in rules are by default universally quantified and ∀ symbol is

dropped for that reason. For instance, the first rule says that if ?Y is a man

and ?X is his father, then ?X has a son who is ?Y for all ?X and ?Y. Similarly

third rule says that if ?Y is a woman and ?X is her mother, then ?Y is ?X’s

daughter.

Once ontology is ready, we can list all the facts as seen in the third part

of Figure-3.22. In the first two facts we learn that Abraham is a man and

Sarah is a woman. In the third fact, we see that Isaac is a man and Abraham

and Sarah are his parents. Beside having explicit facts, we can infer implicit

ones by using deductive inference rules or by inheritance. For instance, since

Jacob is a man and Isaac is his father, we can infer that Jacob is son of Isaac.

Last part of Figure-3.22 is a query. It aims to find all women that Abraham

has sons with.

Some attributes may hold multiple values Abraham[son –>{Isaac,Ishmael}].

From the facts we can infer that Abraham has two sons. In this case, attribute

“son” holds two values: Isaac and Ishmael.

In this simple ontology cardinality of attributes father and mother is

defined as {0:1}. One person can only have one biologic parents and if mother

or father is unknown then it is indicated with 0. Adam and Eve would be

denoted by 0 since they are believed that they do not have any parents.

person[name{1:∗} ∗=>_string] [3]


Example above indicates that name attribute is mandatory for person

object.We can specify cardinality of the attributes as seen above. {1:∗}

indicates that a person at least has one name. ∗=> limits the type for name

attribute with only strings. F-Logic supports XML Schema data types and

the corresponding built-ins such as _string, _integer, _decimal, _iri, _time,

_dateTime, and _duration. The type _iri is for representing International

Resource Identifiers, that are used to denote objects on the Web.

In F-Logic methods are represented and handled as objects without any

distinction. In Figure-3.22 father and jacob are both object names.

?- Abraham[?X ->?].

is a query where we search for all method names for Abraham. The answer

for this query is

?X = son

It does not return mother, daughter, or father because “son” is the only

one attribute has values for the object Abraham. It would return son,mother,

daughter, or father if we used => instead of −>. The last question mark in

the query is “don’t-care” variable.

In F-Logic methods can take parameters and method overloading is legal.

Jacob[son(Leah) ->{Reuben, Simeon, Levi, Judah, Issachar, Zebulun},

son(Rachel) ->{Joseph, Benjamin}, son(Zilpah) ->{Gad, Asher},

son(Bilhah) ->{Dan, Naphtali}].


In the above example, method son is overloaded. We overloaded the

method by using a parameter that indicates mother of the son. This example

shows that Jacob has different sons who are born by different women. When

we query sons of Jacob by:

?- Jacob[son ->?X].

the answer returns all twelve sons: Reuben, Simeon, Levi, Judah, Issachar,

Zebulun, Joseph, Benjamin, Gad, Asher, Dan, Naphtali. It is important to

point out that variables never take a set as a value. Thus, it returns twelve

separate results ?X = Reuben, ?X= Simeon, ?X=Levi, etc. Similarly,

?- Jacob[son(Rachel) ->?X].

yields ?X = Joseph and ?X = Benjamin. ?X is only bounded by a single

individual.

F-Logic allows constructing hierarchical structures by using is-a relation.

Single colon(:) indicates class membership of individuals. For instance:

Abraham:man.

indicates that object Abraham belongs to class man. We can also show

class-subclass relationship by using double colon(::) .

man::person.

Example above states that class man is subclass of class person. Every

member of subclass man is also member of class person.

F-molecules can be used in order to simplify multiple assertions about


the same object.

Isaac:man.

Isaac[father ->Abraham].

Isaac[son ->Jacob].

Isaac[son ->Esau].

All the assertions above can be replaced by a single F-molecule:

Isaac:man[father ->Abraham, son ->{Jacob,Esau}].

Signature-F-atoms are used to indicate schema for classes. The only

syntactic difference of data-F-atoms and signature-F-atoms is that we use

=> symbol instead of ->in signature-F-atoms.

man[son(woman) ∗=> man].

The signature-F-atom above defines the multi-valued method son, that

takes single argument “woman”. This method applies to objects of the class

man. The result of the method must be an object of class man.

Intersection in F-Logic is simply defined by “and” keyword (comma can

be used as shorthand for and). We define a college assistant as both a student

and an employee by using intersection operator as follows:

course[teachingAssistant ∗=>(student and employee)].

Intersection of ranges can also be specified without the intersection opera-


tor:

course[teachingAssistant ∗=> student].

course[teachingAssistant ∗=> employee].

Union in F-Logic is simply defined by “or” keyword (semi-colon can be

used as shorthand for or). For instance an instructor can be a professor or a

lecturer. In order to define such structure we need to use intersection operator

as follows:

course[instructor ∗=>(professor or lecturer)].

We distinguish inheritable methods from non-inheritable ones by adding

∗ to =>. If a method is defined as inheritable (∗=>), then that method can

be applied to sub-classes and instances. On the other hand, if a method is

defined as non-inheritable(=>) then it is only applicable to class it is defined

for.

In Figure-3.22, we see that man is sub-class of person. Thus, man can

inherit all inheritable methods from its super class. For instance:

man[father{0:1}∗=>man, mother{0:1}∗=>woman, daughter ∗=>woman,

son ∗=>man].

Inheritable methods can be inherited to the instances of the classes,

however; then they become non-inheritable as follows:

Isaac[father{0:1} => man, mother{0:1} => woman, daughter =>woman,


son => man].

F-Logic supports predicate symbols called P-atoms. The first predicate

below is 0-ary(nullary) P-atom and the second one is a binary P-atom.

Thing.

married(Isaac,Rebekah).

Predicates expressed by P-atoms can be represented by F-atoms, as shown

below:

Thing[ ].

Isaac[marriedto -> Rebekah].

Dot notation(path expressions) in object oriented languages are seen in

F-Logic as well.

Abraham.son.son

Abraham.son yields a set and the second son is applied to every object in

the set, that is returned by Abraham.son. In short, Abraham.son.son yields

all grandsons of Abraham. Path expressions can also be used in queries as

follows:

?- Abraham.son.son=?X .

?- Abraham.son[son ->?X].

?- Abraham[son ->?Y] and ?Y[son ->?X].

All three queries above yields answer for Abraham’s grandsons.


A programming language Flora-2, a developed version of Flora-1[110], is

developed by using F-logic[57], HiLog[29], and transaction logic [21], that is

used in Ontology management, Knowledge-based networking , Information

integration , Software engineering and Semantic Web. In addition to Flora-2,

Semantic web services language (SWSL)[15] syntax and semantic is also

inspired from F-logic. Thus, F-Logic is a strong candidate for building

ontologies for Semantic Web. Study of Bruijn and Heymans in 2007[27] shows

that RDF, RDFS, and eRDFS can be embedded in F-Logic.

Chapter 4

APPLICATIONS

4.1 The Open Mind Common Sense Project(OMCS)

Although computers are capable of calculating complex operations that an

ordinary adult cannot answer easily such as finding the winning strategy for

a given position in a chess game, or finding shortest travel distance between

departure and destination, or translating speech into text; they are not able to

perform some easier tasks that requires recognizing objects within an image,

drawing simple conclusions about life, or understanding natural language that

a small child could accomplish [93].

The real struggle for machines for not being able to accomplish such easy

tasks is, they are lack of common sense. They do not know or understand

anything about human beings, their lives, their thoughts, their emotions,

their reactions to certain things, and so on. People learn about facts or

relationships by experiencing them and we store this knowledge in our brains.

There are millions of facts that we learn and we do not even put effort in

86

CHAPTER 4. APPLICATIONS 87

order to learn them. For instance, we know that everybody’s parents are

older than themselves, or we know that a giraffe is taller than a cat, or we

know that if we stand under the sun at noon in summer, we will get tanned

or even we may get sunburned. These and many other knowledge most of

the time comes with experience and human brain is able to make inferences

by using millions of these complex knowledge within a short time.

There have been many researches attempting to construct a database for

common knowledge. CYC [67] project has coded 106 commonsense axioms

and entered into CYC’s knowledge base. Some of the common sense axioms

taken from CYC’s database are:

“- You have to be awake to eat.

- You can usually see people’s noses, but not their hearts.

- Given two professions, either one is a specialization of the other or else

they are likely to be independent of one another.

- You cannot remember events that have not happened yet.

- If you cut a lump of peanut butter in half, each half is also a lump of

peanut butter; but if you cut a table in half, neither half is a table.”

Although Lenat succeeded to create such a large database for commonsense

knowledge, they are still far away from listing all hundreds of millions of

commonsense axioms. Handcrafting all axioms is a hassle for a researcher.

On the contrary of CYC Project that uses single team to build up such

large databases. The OMCS Project takes the advantage of distributed

human projects. Project is built on volunteering. Over eight thousand people

volunteered to built database of common sense. Starting from 2000, The


OMCS Project was able to collect only one fourth of the data that CYC had

in two years. However, project is a lot more efficient than CYC in terms of

time and cost.

In 2002 [94], OMCS is evaluated by human judges on approximately 1%

of the corpus. Data is tested for its generality, neutrality, and sense. Results

show that:

- The average rating for generality is 3.26 (1=specific fact, 5=general

truth).

- The average rating for truth is 4.28 (1=false, 5=true), and 67% of

items were rated 5.

- The average rating for neutrality is 4.42 (1=biased, 5=neutral). Based

on this score, can conclude that database is relatively unbiased.

- The average rating for sense is 4.55 (1=makes no sense, 5=makes

complete sense).

- Judges also conclude that 84% of the statements are known by at least

high school level.

By 2007, over 150,000 nodes was automatically created to built the

semantic network called ConceptNet. Although The Open Mind Common

Sense Project takes advantage of using crowd sourcing and being able to build

database for common sense knowledge, it does not guarantee completeness or

soundness. Project concludes having some incorrect and incomplete inferences.


4.2 ConceptNet 3: a Flexible, Multilingual Semantic

Network for Common Sense Knowledge

Much of the researches, that requires understanding natural language depends

on understanding the relationship between concepts, that are used to describe

facts about the world of our interest. While conveying thoughts in natural

language, we make some assumptions and we do not state every fact about

the world based on those assumptions. For instance, when we say " I go to

school by using a train.", that consists of many assumptions. In daily speech

we do not need to specify that in order to take the train, first we swipe our

metro cards. In order to be able to swipe metro cards, we have to fill them

with certain amount that is at least as much as subway fare. Instead of listing

all the requirements to take the train, many people would assume that I was

able to satisfy all conditions that are necessary for going from one location

to the school. Since we do not specify all facts but we assume them, using

an automated way to find all relationships between concepts might not be

complete since automation is not capable of understanding the underlying

assumptions. Many of the lexical resources we currently use such as WordNet,

PropBank, FrameNet, CYC, etc. are constructed without using automated

tools [50].

ConceptNet 3 is developed version of ConceptNet, that is constructed

from the data in free-form or semi-structured frames, where volunteers fill in

the blanks of given sentences.

In this semantic network, nodes represent concepts, and edges between

nodes represent predicates that indicate relationship between concepts. Some


of the relations described in ConceptNet3 are IsA, PartOf, CapableOf, De-

sireOf, CreatedBy, InstanceOf, EffectOf, PropertyOf, MadeOf, LocationOf,

UsedFor, and ConceptuallyRelatedTo for the relationship that are vague.

Figure 4.1: Some of the predicates and sample sentences that generatesthose predicates in ConceptNet 3.1

ConceptNet uses pattern matching algorithm to generate predicates. Each

sentences are compared with predetermined patterns. These patterns indicate

structure of the sentences. Some of the patterns are listed in Figure-4.1.

Those patterns are either captured from predetermined frames which are filled

by users or from a free form of the text.

Open Mind Commons(OMC) is a developed version of OMCS Project

and it is built on top of ConceptNet3. Inference used in OMC returns feedback

to user. User can see what is known by the system so that user can see the

gaps in the knowledge base. If two of the concepts such as X and Y appear in

the same position in equivalent predicates, OCM hypothesizes that these two1Catherine Havasi, Robert Speer, and Jason Alonso. “ConceptNet 3: a flexible, multi-

lingual semantic network for common sense knowledge”. In: Recent advances in naturallanguage processing. John Benjamins Philadelphia, PA. 2007, pp. 27–29.


concepts are similar. Thus, system draw a hypothesis such that any predicate

that is true for concept X, will be true for concept Y as well. OCM turns

this hypothesis into a natural language question form and asks user for the

verification with Yes/No questions.

In addition to Yes/No questions, if OCM has lack of knowledge on certain

concept compared to what it already knows about similar concepts, it can

ask user fill in the blank type of questions to learn more about that concept.

Figure 4.2: Knowledge about ocean.2

Each predicate has a score of validity. This score is calculate user feedback

or user entrance. If multiple user enters the same predicate that increases2See footnote 1.


the validity score of the predicate. Or user manually can evaluate truthness

of a statement and it alters the validity score of a predicate. Based on [50],

the highest-scored predicate in the English is “Dogs are a kind of animal”,

asserted by 101 different users.

In addition to reliability score, ConceptNet 3 has a polarity degree that

ranges between -1 and 1. Polarity degree is used to detect negation in

statements such as “People don’t want to be hurt” [50].

Unlike OMCS evalutated by human judge, ConceptNet 3 is evaluated by

comparing its IsA, PartOf, and UsedFor relations with similar lexical resources

such as WordNet and BSO. IsA, PartOf, and UsedFor tested on predicates,

whose both concepts consist a single non-stop word in ConceptNet 3. If

similar relation is seen in WordNet or The Brandeis Semantic Ontology(BSO),

that predicate is marked as “hit”; otherwise it is marked as “miss”. If tested

predicate does not exist in other databases then that predicate marked as “no

comparison”.

Figure 4.3

Figure 4.3 shows comparisons of ConceptNet with WordNet and BSO. Test

predicate is marked as “hit” if both concepts exists and the relationship holds

in WordNet or BSO. Test predicate marked as “miss” when both concepts

exists but relationship does not hold. And test predicate marked as “no


comparison” when either one or both concept does not exist in the target

database.

Figure 4.4

Figure 4.4 indicates percentage of overlapping ConceptNet predicates with

WordNet and BSO. In addition to IsA, PartOf, UsedFor relations, ConceptNet

can also express other relations such as “fire can burn you” (CapableOf), “you

would find books at a library” (LocationOf), and “an effect of opening a gift

is surprise” (EffectOf) [50].


4.3 WordNet

Dictionaries and thesauruses are very early linguistic tools used for linguistics

and natural language processing. A dictionary contains alphabetically ordered

list of words, their meanings, example sentences about the meaning of the

words, their phonetic information in any languages. A thesaurus is book that

contains list of words in groups of synonyms and related concepts. Thesauri are

the least formal form of an ontology[35] and WordNet is the most well-known

example for the thesauri.

WordNet is a manually constructed online hierarchical lexical database

for English nouns, verbs, adjectives and adverbs[75, 37]. This database

consists of synonym sets(synsets), where each synset contains lexically and

semantically close words or phrases of a concept. WordNet can be considered

as a combination of a dictionary and a thesaurus since it provides short

definitions and usage of words and groups words based on their meanings,

however; dictionaries and thesauruses are not in a machine processable format.

If a word is polysemous(has more than one sense), it appears in different

synsets. Table-4.1 shows number of unique strings, synsets and word-sense

pairs for nouns, verbs, adjectives, and adverbs.

POS Unique Strings Synsets Word-SensePair

Noun 117798 82115 146312Verb 11529 13767 25047Adjective 21479 18156 30002Adverb 4481 3621 5580Totals 155287 117659 206941

Table 4.1: Statistics of WordNet3.0[107]


Figure 4.5: Semantic Relations in WordNet[75]

Figure-4.5 shows semantic relations in WordNet. The main lexical relation

in WordNet is synonymy. Word sharing the same or similar meaning are

considered as synonyms such as a pipe and a tube. Another relation is

antonym. Words sharing the opposite meanings are antonyms such as wet

and dry. Hyponymy is a relation between a generic term and a specific

term. Other terms for hyponymy are ISA, or hypernomy or subsumption. For

instance, sugar maple is a maple. Hyponymy in WordNet builds a hierarchical

tree between synsets. Meronymy indicates part-of relation. For instance, a

wheel is meronymy of a car. Synonym and antonymy relations can be seen


in all form of the word(noun, verb, adjective, and adverb). Hyponymy and

meronymy are seen between nouns. And troponomy and entailment are only

applicable to verbs.

Figure 4.6: A noun tree for deceiver in WordNet[38]


Figure 4.7: A verb tree for deceive in WordNet[38]


Figure 4.8: An adjective cluster for words wet and dry in WordNet[38]


4.4 FrameNet

FrameNet[12] is a human- and machine-readable lexical database for English,

based on annotating examples of how words are used in actual texts[11].

Although FrameNet started as a toy project, having more than 200,000

manually annotated sentences linked to more than 1,200 semantic frames

makes FrameNet intensively used in information extraction, machine transla-

tion, event recognition, and sentiment analysis applications. However, these

numbers are still less than annotations in WordNet and any other lexical

databases.

Frames are generalizations of group of words that are syntactically and

semantically related[11]. A frame consists of frame elements(FEs), that

are basically roles and lexical units(LUs), that are words evoke that frame.

Lexical units are senses of the head word[5]. LUs include informal definitions

and POS tags. FrameNet is developed based on frame semantics [40]. Frame

semantic based on the idea that one cannot understand an event without

knowing relation, or entity and the participants in it. For instance, in order

to understand the action “Cooking”, a person needs to understand FEs “Food”

being cooked, the “Cook” who will do the cooking action, the “Container”

where the food will be cooked in, source of heat “Heating_instrument” needs

to be understood. All other words that invoke this frame such as fry, bake,

boil, and broil, are lexical units.


Figure 4.9: Commerce_buy Frame

Fig-4.9 is a popular example used to demonstrate a schematic represen-

tation of buying action involving various participants, and other conceptual

roles.

Figure 4.10: Frame elements of Commerce_buy Frame

Fig-4.10 contains FEs with an example that explains in what context


those FEs are used, and Fig-4.11 contains FUs of Commerce_buy Frame.

Figure 4.11: Frame units of Commerce_buy Frame

FrameNet is applied to other languages to create FrameNet-style lexicons

for other languages such as French, Chinese, German, Brazilian, Spanish,

Japanese, Korean, and Swedish. Besides creating FrameNet-style lexicons

for other languages, it inspired several other projects in specialized domains

such as Soccer FrameNet, Suggested Upper-Merged Ontology (SUMO), and

BioOntoFN at Linköpings Universitet.


4.5 VerbNet

Researches attempted to create verb lexicon for verbs in English such as

Levin’s in 1993 classified verbs based on their syntactical alternation[68, 102,

59, 92]. Levin’s verb classification falls short of assigning semantic components

to each class. VerbNet is extension of Levin’s verb classes. It is a class-based

approach to create a verb lexicon that makes explicit the close association

between syntax and semantics. Preserving both syntactic and the semantic

relation is important for creating natural language processing applications

such as machine translation and information extraction.

In VerbNet classes are organized in a way that every verb in each classes

shares a common semantic, a common syntactic frames and common thematic

roles[59]. Table-4.2 shows the syntactic frames allowed for the hit class that

consists of verbs like hit, kick, slap, tap, etc.

Events are tripartite structures consists of three time function during(E ),

end(E ) and result(E ) for each event E. It is important to distinguish the

state of an object during an event, culmination of the event and after the

action. This tripartite structure allows to express the semantics of change of

state verbs such as verb break.

Table-4.2 is an example entry in VerbNet. V in the table indicates the

verb. Besides verbs, hit class shown in Table-4.2 allows three thematic roles.

Agent(A) is animate, Patient(P) is concrete(can be animate or inanimate),

and Instrument(I) is concrete or inanimate [59]. Thematic roles are used

to describe lexical and semantic relationship between a predicate and its


arguments. There are eleven theme roles defined in [92]: agent, patient,

theme, experiencer, stimulus, instrument, location, source, goal, recipient,

and benefactive.


Type Frame PredicatesBasic Transitive A V P manner(during(E),directedmotion,A)

∧ manner(end(E), forceful,A)∧ contact(end(E),A,P)

Transitive withInstrument

A V P with I manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)

Togetherreciprocal

A V P[+plural] to-gether

manner(during(E),directedmotion,Pi )∧ manner(during(E),directedmotion,Pj )∧ manner(end(E),forceful,Pi )∧ manner(end(E),forceful,Pj )∧ contact(end(E),Pi,Pj)

Resultative A V P Adj manner(during(E),directedmotion,A)∧ manner(end(E),forceful,A)∧ contact(end(E),A,P)∧ Pred(result(E),P)

Resultative A V P Adj with I manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)∧ Pred(result(E),P)

Resultative A V P PP manner(during(E),directedmotion,A)∧ manner(end(E),forceful,A)∧ contact(end(E),A,P)∧ Pred(result(E),P)

Resultative A V P PP with I manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)∧ Pred(result(E),P)

Conative A V at P manner(during(E),directedmotion,A)Conative A V at P with I manner(during(E),directedmotion,I)With/againstalternation

A V I against/onP

manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)

Body-part objector reflexive object

A V I[+body-part/+refl]

manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,?)

Body-part objector reflexive object

A V I[+body-part/+refl]against/on P

manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)

Transitive I V P manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)

Resultative I V P Adj manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)∧ Pred(result(E),P)

Resultative I V P PP manner(during(E),directedmotion,I)∧ manner(end(E),forceful,I)∧ contact(end(E),I,P)∧ Pred(result(E),P)

Table 4.2: Example entry for the Hit class[59]


The example “John hit the sticks together.” requires a plural direct

object and the lexical item “together”. Or the example “John kicked the door

into an open position.” requires the resultative constructions incorporate

a prepositional phrase(PP). In “John hit the stick(I) against the fence(P)”

requires a prepositional phrase “against/on Patient”.

Semantics of frames are shown by conjunctions of each predicate. For

instance, manner(during(E),directedmotion,X) indicates that during event E,

the agent(or the instrument) is in a motion. Similarlymanner(end(E),forceful,X)

∧ contact(end(E),X,P) indicates that the agent (or the instrument) establishes

contact with the patient in a forceful way at the end of event E. Predicate

Pred(result(E),P) indicates that resulting state is achieved by Patient P [59].

VerbNet has hierarchical structure. For instance, The Transfer of a

Message verb class has three layers. Class members in the first layer are

verbs such as ask, cite, demonstrate, dictate, etc. Agent(A), Recipient(R),

and Theme(T) are the thematic roles defined in this layer. Both the agent

and the recipients are animate, and theme is the message. There are two

transitive frames. Frames and predicates are shown for the level-1 below:

Frame PredicatesTransitive withTheme

A V T transfer_info(during(E),A,?,T)

Theme and Recipient A V T to R transfer_info(during(E),A,R,T)

Table 4.3: An example entry for Transfer of a Message - level 1 class [59]

“John explained trigonometry” can be an example to the first frame and

“John taught math to Mary” can be example to the second frame in Table-4.3.


Level-1 class is the parent of Level-2 class. Verbs in the second level of

Transfer of a Message such as ask, dictate, quote, read, show, teach, tell,

write, etc. inherits frames and predicates from its parent class. In addition to

those frames and predicates they can take ditransitive frames as listed below:

Frame PredicatesDitransitive A V R T transfer_info(during(E),A,R,T)

Table 4.4: An example entry for Transfer of a Message - level 2 class [59]

The third level class can be defined by taking the subset of member verbs

ask, tell, show, etc. with another transitive frame with Recipient as direct

object.


4.6 The Brandeis Semantic Ontology (BSO)

Brandeis Semantic Ontology (BSO) is a large lexicon ontology and lexical

database depends on Generative Lexicon (GL)[85], which is a theory of

linguistic semantics which focuses on the distributed nature of compositionality

in natural language [86, 50].

The ontology has three major types: entity, event, and property, each of

which has sub-types: natural, artifactual, and complex. Natural type has

concepts consist of reference only to Formal and Constitutive qualia roles.

Artifactual consists concepts makes reference to purpose, function, or origin.

Complex type consists concepts integrating reference to a relation between

types.

A qualia is a structure that expresses the componential aspect of a word’s

meaning. They represent the connections and relations between words[49].

There are four qualia relations : formal, constitutive, telic, agentive. Qualia

roles are relations, that characterize the relationships between words in the

lexicon. Formal qualia is the basic type distinguishing the meaning of a

word. Constitutive qualia is the relation between an object and its parts.

Telic qualia is the purpose or function of the object. Agentive qualia is the

factors involved in the object’s origins.

Qualia information is retrieved from the British National Corpus (BNC)

and ConceptNet[69]. BSO and ConceptNet are quite similar in terms of

qualia relations. IsA relation in ConceptNet is similar to formal qualia in

BSO, PartOf relation in ConceptNet is similar to the constitutive in BSO,


UsedFor relation is similar to the telic in BSO. CapableOfReceivingAction

relation in ConceptNet is more general than the agentive relation in BSO,

but still includes agentive relations[50].

physobj(x)

FORMAL = physform(x)

artifact obj(x)

FORMAL = physform(x)

TELIC = Pred(E,y,x)

Object x in the example above, is a simple natural physical object on

the left hand side. And it is formed into an artifactual type on the right

hand side by giving it a function(telic role). Artifactual types carry more

information such as their use and purpose than natural types. For instance,

Pred(E,y,x) above is a constraint on its telic value. Pred(E,y,x) denotes a

process E, between an individual y and the physical object x[86].

The following examples, we see how some entries in the BSO look[86]:

1)

[[drink activity]]supertype = [[Take Nourishment Activity]]#subject = [[Animate Living Entity]]#object = [[Beverage]]

2)

’drink’ type = [[Drink Activity]]

3)

’chug’type = [[Drink Activity]]#object = [[Alcoholic Beverage]]

4)

[[Writer]]#telic = [[Write Activity]]

5)

[[Write Activity]]#object = [[Book]]

6)

’novelist’type = [[Writer]](#telic -> #object) = [[Novel]]

Chapter 5

CONCLUSION

In this survey, we briefly summarize evolution of world wide web ever since

its invention by Berners Lee, we discuss the architecture of semantic web.

We introduce semantic web layers and World Wide Web Consortium (W3C)

standardization for semantic web architecture. Further, we discuss knowledge

in computer science point of view. This paper mainly presents different kind

of knowledge representation methodologies, but mostly focuses on Description

Logics(DLs), since DLs is one of the W3C standards for representing the

knowledge to construct ontologies for semantic web. Finally, we introduce

some ontology applications in different formalities.

109

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