Download - Knowledge Representation
Knowledge Representation
كاهاني دكترمحسنhttp://www.um.ac.ir/~kahani/
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Knowledge and its Meaning
Epistemology Types of Knowledge Knowledge Pyramid
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Epistemology the science of knowledge
EPISTEMOLOGY ( Gr. episteme, "knowledge"; logos, "theory"),
branch of philosophy concerned with the theory of knowledge. The main problems with which epistemology is concerned are the definition of knowledge and related concepts, the sources and criteria of knowledge, the kinds of knowledge possible and the degree to which each is certain, and the exact relation between the one who knows and the object known.
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Knowledge Definitionsknowlaedge \'nS-lij\ n [ME knowlege, fr. knowlechen to acknowledge, irreg. fr. knowen ] (14c) 1 obs : cognizance 2 a (1) : the fact or condition of knowing something with familiarity gained through experience or
association (2) : acquaintance with or understanding of a science, art, or technique b (1) : the fact or condition of being aware of something (2) : the range of one's information or understanding <answered to the best of my 4> c : the circumstance or condition of apprehending truth or fact through reasoning : cognition d : the fact or condition of having information or of being learned <a man of unusual 4> 3 archaic : sexual intercourse 4 a : the sum of what is known : the body of truth, information, and principles acquired by mankind b archaic : a branch of learning syn knowledge, learning, erudition, scholarship mean what is or can be
known by an individual or by mankind. knowledge applies to facts or ideas acquired by study, investigation, observation, or experience <rich in the knowledge of human nature>. learning applies to knowledge acquired esp. through formal, often advanced, schooling <a book that demonstrates vast learning >. erudition strongly implies the acquiring of profound, recondite, or bookish learning <an erudition unusual even in a scholar>. scholarship implies the possession of learning characteristic of the advanced scholar in a specialized field of study or investigation <a work of first-rate literary scholarship >.
[Merriam-Webster, 1994]
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Types of Knowledge a priori knowledge
comes before knowledge perceived through senses considered to be universally true
a posteriori knowledge knowledge verifiable through the senses may not always be reliable
procedural knowledge knowing how to do something
declarative knowledge knowing that something is true or false
tacit knowledge knowledge not easily expressed by language
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Knowledge in Expert Systems
Conventional Programming
Knowledge-Based Systems
Algorithms + Data Structures
= Programs
Knowledge+ Inference
= Expert System
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Review of Knowledge Representation Criteria
Definition of Knowledge Representation: A formalism for representing in a computer,
facts and other kinds of knowledge about a subject or specialty such that these facts and knowledge can be used in reasoning.
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Criteria of Adequacy:Metaphysical Adequacy
The representation scheme cannot contradict the actual, real world circumstance, either by ignoring certain things that actually happen or by allowing things to happen that do not.
An expert system is a representation of the real world, therefore it must reflect the real world.
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Epistemic Adequacy
The K.R. scheme must be able to represent facts, usually about individuals and their relations and attributes.
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Heuristic Adequacy
The K.R. scheme must be able to express the reasoning used to solve a problem. Probably the most difficult of these criteria to meet.
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Computational Tractability
The K.R. scheme must be able to manipulate the representation using a computer system.
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Expressiveness
These criteria are "nice", but not necessary. Adequacy criteria are necessary
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Lack of Ambiguity
only one interpretation
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Clarity
Can humans understand what is being said as well as the computer?
Can take this further: we would like the use of the KR to increase or clarify our knowledge of the domain.
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Uniformity
Able to handle all types of knowledge we need to represent in a uniform fashion.
Difficult to represent every type of knowledge (heuristic vs fact, etc) in a different manner.
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Notational convenience
does the knowledge fit the representation? is the developer comfortable with the
representation scheme?
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Declarativeness not procedural, "processing" should not change or
impact the meaning. A representation is declarative if:
the meanings of the statements are independent of the use made of the statements
referential transparency also exists. Referential transparency exists when equivalent expressions can always be substituted for one another while preserving the truth value of the statements in which they occur.
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Knowledge Representation Methods
Production Rules Structured Objects
Semantic Nets Frames
Logic
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Production Rule Representations
Consists of <condition,action> pairs Agent checks if a condition holds
If so, the production rule “fires” and the action is carried out This is a recognize-act cycle
Given a new situation (state) Multiple production rules will fire at once Call this the conflict set Agent must choose from this set
Call this conflict resolution Production system is any agent
Which performs using recognize-act cycles
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Case Studies Production Rules sample domains
e.g. theorem proving, determination of prime numbers, distinction of objects (e.g. types of fruit, trees vs. telephone poles, churches vs. houses, animal species)
suitability of production rules basic production rules
no salience, certainty factors, arithmetic rules in ES/KBS
salience, certainty factors, arithmetic e.g. CLIPS, Jess
enhanced rules procedural constructs
e.g. loops objects
e.g. COOL, Java objects fuzzy logic
e.g. FuzzyCLIPS, FuzzyJ
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Advantages of Production Rules
simple and easy to understand straightforward implementation
in computers possible formal foundations for some
variants
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Problems with Production Rules
simple implementations are very inefficient
some types of knowledge are not easily expressed in such rules
large sets of rules become difficult to understand and maintain
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Semantic Nets graphical representation for propositional information originally developed by M. R. Quillian as a model for
human memory labeled, directed graph nodes represent objects, concepts, or situations
labels indicate the name nodes can be instances (individual objects) or classes
(generic nodes) links represent relationships
the relationships contain the structural information of the knowledge to be represented
the label indicates the type of the relationship
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Example
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Relationships without relationships, knowledge is an unrelated
collection of facts reasoning about these facts is not very interesting
inductive reasoning is possible relationships express structure in the collection of
facts this allows the generation of meaningful new
knowledge generation of new facts generation of new relationships
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Types of Relationships relationships can be arbitrarily defined by the knowledge
engineer allows great flexibility for reasoning, the inference mechanism must know how
relationships can be used to generate new knowledge inference methods may have to be specified for every
relationship frequently used relationships
IS-A relates an instance (individual node) to a class (generic node)
AKO (a-kind-of) relates one class (subclass) to another class (superclass)
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Objects and Attributes attributes provide more detailed information on
nodes in a semantic network often expressed as properties
combination of attribute and value attributes can be expressed as relationships
e.g. has-attribute
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Implementation Questions simple and efficient representation schemes for
semantic nets tables that list all objects and their properties tables or linked lists for relationships
conversion into different representation methods predicate logic
nodes correspond variables or constants links correspond to predicates
propositional logic nodes and links have to be translated into propositional
variables and properly combined with logical connectives
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OAV-Triples object-attribute-value triplets
can be used to characterize the knowledge in a semantic net
quickly leads to huge tables
Object Attribute Value
Astérix profession warrior
Obélix size extra large
Idéfix size petite
Panoramix wisdom infinite
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Problems Semantic Nets expressiveness
no internal structure of nodes relationships between multiple nodes no easy way to represent heuristic information extensions are possible, but cumbersome best suited for binary relationships
efficiency may result in large sets of nodes and links search may lead to combinatorial explosion
especially for queries with negative results usability
lack of standards for link types naming of nodes
classes, instances
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Frame represents related knowledge about a subject
provides default values for most slots frames are organized hierarchically
allows the use of inheritance knowledge is usually organized according to cause and effect
relationships slots can contain all kinds of items
rules, facts, images, video, comments, debugging info, questions, hypotheses, other frames
slots can also have procedural attachments procedures that are invoked in specific situations involving a
particular slot on creation, modification, removal of the slot value
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Simple Frame ExampleSlot Name Filler
name Astérix
height small
weight low
profession warrior
armor helmet
intelligence very high
marital status presumed single
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Overview of Frame Structure two basic elements: slots and facets (fillers, values, etc.); typically have parent and offspring slots
used to establish a property inheritance hierarchy (e.g., specialization-of)
descriptive slots contain declarative information or data (static knowledge)
procedural attachments contain functions which can direct the reasoning process (dynamic
knowledge) (e.g., "activate a certain rule if a value exceeds a given level")
data-driven, event-driven ( bottom-up reasoning) expectation-drive or top-down reasoning pointers to related frames/scripts - can be used to transfer control to
a more appropriate frame
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Slots each slot contains one or more facets facets may take the following forms:
values default
used if there is not other value present range
what kind of information can appear in the slot if-added
procedural attachment which specifies an action to be taken when a value in the slot is added or modified (data-driven, event-driven or bottom-up reasoning)
if-needed procedural attachment which triggers a procedure which goes out to get information
which the slot doesn't have (expectation-driven; top-down reasoning) other
may contain frames, rules, semantic networks, or other types of knowledge
[Rogers 1999]
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Usage of Frames filling slots in frames
can inherit the value directly can get a default value these two are relatively inexpensive can derive information through the attached
procedures (or methods) that also take advantage of current context (slot-specific heuristics)
filling in slots also confirms that frame or script is appropriate for this particular situation
[Rogers 1999]
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Restaurant Frame Example generic template for restaurants
different types default values
script for a typical sequence of activities at a restaurant
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Generic Restaurant FrameGeneric RESTAURANT Frame
Specialization-of: Business-EstablishmentTypes: range: (Cafeteria, Fast-Food, Seat-Yourself, Wait-To-Be-Seated) default: Seat-Yourself if-needed: IF plastic-orange-counter THEN Fast-Food, IF stack-of-trays THEN Cafeteria, IF wait-for-waitress-sign or reservations-made THEN Wait-To-Be-Seated, OTHERWISE Seat-Yourself.Location: range: an ADDRESS if-needed: (Look at the MENU)Name: if-needed: (Look at the MENU)Food-Style: range: (Burgers, Chinese, American, Seafood, French) default: American if-added: (Update Alternatives of Restaurant)Times-of-Operation: range: a Time-of-Day default: open evenings except MondaysPayment-Form: range: (Cash, CreditCard, Check, Washing-Dishes-Script)Event-Sequence: default: Eat-at-Restaurant ScriptAlternatives: range: all restaurants with same Foodstyle if-needed: (Find all Restaurants with the same Foodstyle)
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Frame Advantages fairly intuitive for many applications
similar to human knowledge organization suitable for causal knowledge easier to understand than logic or rules
very flexible
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Frame Problems it is tempting to use frames as definitions of concepts
not appropriate because there may be valid instances of a concept that do not fit the stereotype
exceptions can be used to overcome this can get very messy
inheritance not all properties of a class stereotype should be
propagated to subclasses alteration of slots can have unintended consequences in
subclasses
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Introduction to Logic expresses knowledge in a particular mathematical notation All birds have wings --> x. Bird(x) -> HasWings(x) rules of inference
guarantee that, given true facts or premises, the new facts or premises derived by applying the rules are also true
All robins are birds --> x Robin(x) -> Bird(x) given these two facts, application of an inference rule gives:
x Robin(x) -> HasWings(x)
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Logic and Knowledge rules of inference act on the superficial structure or syntax
of the first 2 formulas doesn't say anything about the meaning of birds and robins could have substituted mammals and elephants etc.
major advantages of this approach deductions are guaranteed to be correct to an extent that
other representation schemes have not yet reached easy to automate derivation of new facts
problems computational efficiency uncertain, incomplete, imprecise knowledge
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Summary of Logic Languages propositional logic
facts true/false/unknown
first-order logic facts, objects, relations true/false/unknown
temporal logic facts, objects, relations, times true/false/unknown
probability theory facts degree of belief [0..1]
fuzzy logic degree of truth degree of belief [0..1]
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Syntax of Propositional Logic
A BNF (Backus-Naur Form) grammar of sentences in propositional logic
Sentence -> AtomicSentence | ComplexSentence
AtomicSentence -> True | False | P | Q | R | ...
ComplexSentence -> (Sentence) | Sentence Connective Sentence | ~Sentence
Connective -> ^ | V | <=> | =>
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Inference Rules more efficient than truth tables
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Modus Ponens eliminates => (X => Y), X ______________ Y
If it rains, then the streets will be wet. It is raining. Infer the conclusion: The streets will be wet.
(affirms the antecedent)
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Modus tollens (X => Y), ~Y _______________ ¬ X
If it rains, then the streets will be wet. The streets are not wet. Infer the conclusion: It is not raining.
NOTE: Avoid the fallacy of affirming the consequent: If it rains, then the streets will be wet. The streets are wet. cannot conclude that it is raining.
If Bacon wrote Hamlet, then Bacon was a great writer. Bacon was a great writer. cannot conclude that Bacon wrote Hamlet.
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Syllogism chain implications to deduce a conclusion) (X => Y), (Y => Z) _____________________ (X => Z)
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Resolution
(X v Y), (~Y v Z) _________________ (X v Z) basis for the inference mechanism in the Prolog
language and some theorem provers
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Complexity issues truth table enumerates 2n rows of the table for any proof
involving n symbol it is complete computation time is exponential in n
checking a set of sentences for satisfiability is NP-complete but there are some circumstances where the proof only involves
a small subset of the KB, so can do some of the work in polynomial time
if a KB is monotonic (i.e., even if we add new sentences to a KB, all the sentences entailed by the original KB are still entailed by the new larger KB), then you can apply an inference rule locally (i.e., don't have to go checking the entire KB)
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Predicate Logic new concepts (in addition to propositional logic)
complex objects terms
relations predicates quantifiers
syntax semantics inference rules usage
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Objects distinguishable things in the real world
people, cars, computers, programs, ... frequently includes concepts
colors, stories, light, money, love, ... properties
describe specific aspects of objects green, round, heavy, visible,
can be used to distinguish between objects
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Relations establish connections between objects relations can be defined by the designer or user
neighbor, successor, next to, taller than, younger than, …
functions are a special type of relation non-ambiguous: only one output for a given
input
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Syntax also based on sentences, but more complex
sentences can contain terms, which represent objects constant symbols: A, B, C, Franz, Square1,3, … stand for unique objects ( in a specific context)
predicate symbols: Adjacent-To, Younger-Than, ... describes relations between objects
function symbols: Father-Of, Square-Position, … the given object is related to exactly one other object
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Semantics provided by interpretations for the basic constructs
usually suggested by meaningful names constants
the interpretation identifies the object in the real world predicate symbols
the interpretation specifies the particular relation in a model may be explicitly defined through the set of tuples of objects that satisfy the
relation function symbols
identifies the object referred to by a tuple of objects may be defined implicitly through other functions, or explicitly through tables
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Terms logical expressions that specify objects constants and variables are terms more complex terms are constructed from function
symbols and simpler terms, enclosed in parentheses basically a complicated name of an object
semantics is constructed from the basic components, and the definition of the functions involved either through explicit descriptions (e.g. table), or
via other functions
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Unification an operation that tries to find consistent variable
bindings (substitutions) for two terms a substitution is the simultaneous replacement of variable
instances by terms, providing a “binding” for the variable without unification, the matching between rules would be
restricted to constants often used together with the resolution inference rule unification itself is a very powerful and possibly complex
operation in many practical implementations, restrictions are imposed
e.g. substitutions may occur only in one direction (“matching”)
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Atomic Sentences state facts about objects and their relations specified through predicates and terms
the predicate identifies the relation, the terms identify the objects that have the relation
an atomic sentence is true if the relation between the objects holds this can be verified by looking it up in the set of
tuples that define the relation
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Complex Sentences logical connectives can be used to build more
complex sentences semantics is specified as in propositional logic
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Quantifiers can be used to express properties of collections
of objects eliminates the need to explicitly enumerate all
objects predicate logic uses two quantifiers
universal quantifier existential quantifier
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Universal Quantification states that a predicate P is holds for all objects
x in the universe under discourse x P(x)
the sentence is true if and only if all the individual sentences where the variable x is replaced by the individual objects it can stand for are true
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Existential Quantification states that a predicate P holds for some objects
in the universe x P(x)
the sentence is true if and only if there is at least one true individual sentence where the variable x is replaced by the individual objects it can stand for
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Horn clauses or sentences class of sentences for which a polynomial-time
inference procedure exists P1 P2 ... Pn => Q
where Pi and Q are non-negated atomic sentences
not every knowledge base can be written as a collection of Horn sentences
Horn clauses are essentially rules of the form If P1 P2 ... Pn then Q
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Comparison Between Knowledge
Representation Schemes
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Similarity Despite everything, there are many similarities
between the three knowledge representation schemes.
All express a binary relationship between two objects: entity-attribute-triples in production rules, instance-slot-filler in structured objects, and relationship between two parameters in predicate logic.
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Similarity Production rules and structured objects are considered
more object centered, while logic is considered more relationship centered, but we can map from one to the other.
Predicate logic makes is easier to represent non-binary relationships, other formalisms require the creation of a linking entity.
Frames overcome some of the complexity by grouping like information together).
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Similarity
With respect to the first three criteria (metaphysical, epsitemic, and heuristic) each representation scheme is adequate.
With respect to the fourth criteria (computational tractability), Predicate logic has some unique qualities (discuss shortly).
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Production Rules
High notational convenience. Programmers are very comfortable working
with production rules. More expert systems have used production rules
than other knowledge representation schemes
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Structured Objects
The biggest problem is default reasoning, which creates a great deal of trouble. the ability to "inherit properties" from object
more highly placed in the hierarchy Ironically, the ability to handle default
reasoning was part of the initial attraction of these representation
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Structured Objects
When we attempt to implement "exception processing" we lose the ability to express universal truths!
Not much use to have a knowledge base that cannot express universal truths within its domain!
Best problems such as taxonomizing.
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Predicate Logic
Special issues with respect to computational tractability.
We limit Logic Representation to Horn Clauses so that logic more computationally tractable.
The question is whether or not we lost "expressiveness" by limiting to Horn clauses.
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Predicate Logic
Limit predicate calculus in two ways:
1. only one literal on the left hand side of the clause
2. cannot have negated literals
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Predicate Logic - One Problem:
Treat negation as failure. conclude that a literal is false unless we show it to be
true. This a closed world assumption
when all our predicates are taken together we know the necessary conditions for the truth of the predicate.
This seems reasonable, but consider trying to enumerate the conditions for things like: birds that don't fly, etc.
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Predicate Logic With negation as failure
must know how our knowledge base is going to be used (what sort of deductions it must make) so that we present the predicates properly (we may need to order them in a particular way).
Difficult to envision every eventuality. Loose the declarative nature of logic. Can no longer interpret the knowledge "neutrally".
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Predicate Logic - Second Problem:
Lose the non-monotonic nature of the reasoning process. In a monotonic system if a certain conclusion can be
drawn from a body of evidence, then adding to the evidence cannot prevent the conclusion from being drawn.
KB |- P then KB + delta |- P for any delta. By interpreting negation as failure, we lose the non-
monotonic nature that classical logic allows us.
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Predicate Logic
Structured objects using an inheritance property appear to avoid this issue, but the problems of default values in reasoning leads to another set of problems.
With respect to Predicate Logic, can conclude that its expressiveness is adequate, but be aware of the limitations.
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Predicate Logic There are similar problems with the other knowledge
representation schemes with respect to negation. What is meant by the absence of a relationship
between to objects in a semantic network? Is there NO relationship or simply lack of knowledge
about the existence of a relationship. With the closed-world assumption, the lack of link
means that the relationship does not exist.
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Choosing a way to represent knowledge
The nature of the search space The nature of the data The nature of the knowledge
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The nature of the search space
If some basic problem solving approach will work (i.e. a brute force approach that explicitly examines all alternatives), then use it! If the problem space is relatively small and data
and rules are reliable, exhaustive search via Prolog or Lisp may be best.
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The nature of the search space
Consider ways to factor the search space. ”Pruning" branches that are unlikely Decomposing the domain into independent
components that can be processes separately
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The nature of the data If the data has some inherent structure to it, you
may be able to fit it to a structured object representation easily.
Static knowledge is generally easier to use with structured objects than dynamic knowledge (dynamic knowledge changes during the execution of the program).
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The nature of the data Consider use multiple representation schemes to
represent all of the knowledge. Be careful how you organize the knowledge in the
knowledge base. ”Declarativeness", is rarely achieved. Therefore, when executing the system, the ordering of
knowledge within the knowledge base may affect the solution, certainly the solution path.
دانش مهندسي و خبره -سيستمهاي
كاهاني دكتر
The nature of the knowledge
Is the reasoning along the lines of this and that and this other thing suggest A
production rules with certainty factors are in order
Or is it more categorical as with standard logic
دانش مهندسي و خبره -سيستمهاي
كاهاني دكتر
Summary Despite all the work being done on knowledge
representation, there is relatively little advice on how to pick a knowledge representation scheme.
Even when using a shell, do not ignore the differences between knowledge representation schemes, otherwise you may end up with an unusable expert systems.