logics for data and knowledge representation semantic matching
TRANSCRIPT
Logics for Data and KnowledgeRepresentation
Semantic Matching
Outline Introduction:
Why matching? The matching problem
Kinds of matching: Syntactic versus Semantic Steps in matching Kinds of schemas
S-Match MinSMatch
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Approaching the heterogeneity problem Knowledge can be represented using graphs. These graphs can be very different:
Different structure (RDBs, OODB, XML, thesauri, formal ontologies)
Different conceptualizations: they reflect different visions of the world
They contain different terminology and polysemous terms They have different degrees of specificity, scope and coverage They can be expressed in different languages
Heterogeneity of these graphs demands the exposition of relations between them, such as semantically equivalent.
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The Matching Problem Matching Problem: given two finite graphs, finds all nodes in
the two graphs that syntactically or semantically correspond to each other.
Given two graph-like structures (e.g., classifications, XML and database schemas, ontologies), a matching operator produces a mapping between the nodes of the graphs.
Solution: A possible solution consists in the conversion of the two graphs in input into lightweight ontologies and then matching them semantically.
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A Matching Problem
?
?
?
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Kinds of Matching: Syntactic versus Semantic (I) Syntactic matching
Matching of nodes as objects or strings (without meaning)
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“Virus” partially matches with “Computer virus”“Wives” is an exceptional form for “Wife”
Semantic matching
Matching of nodes as concepts
“Car” is equivalent to “Automobile” Car ≡ Automobile“Dog” is more specific than “Animal” Dog ⊑ Animal
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Kinds of Matching: Syntactic versus Semantic (II) Syntactic matching
Relations are computed between labels at nodes.
The similarity is given in a range [0,1].
Most of the tools developed so far are syntactic.
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Semantic matchingRelations are computed between concepts at nodes.
They return a semantic similarity, namely R {∈ , ≡, , , ⊑ ⊒ ⊓}, sometimes with a confidence value in the range [0,1].
There are a few tools of this kind, but they are recently increasing. They return different kinds of semantic relations.
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Steps in matching A matching problem can be decomposed in three steps:
1. Extract the graphs from the conceptual models under consideration;
2. Convert the graphs into formal ontologies
3. Match the formal ontologies
In the next slides we show some examples of step 1
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Relational DB Schemas Let us consider the following relational database (RDB)
model, say “BANK”:
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We can represent the RDB model “BANK” as a graph (i.e. a tree) with root “BANK”.
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Relational DB Schemas: Representation #1 The RDB model is first partitioned into relations, then
attributes and data instances.
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Relational DB Schemas: Representation #2 The model is partitioned into relations, then into tuples,
attributes and data instances.
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Relational DB Schemas: notes Which of the two representations is more preferable
depends on the concrete task.
It is always possible to transform one representation into the other.
In contrast to the example of RDB “BANK”, DB schemas are seldom trees. More often, DB schemas are translated into Directed Acyclic Graphs (DAG’s) and then approximated into trees.
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OODB Schemas Let us consider the RDB “BANK” in terms of an object-oriented DB (OODB) schema:
BRANCH (Street, City, Zip) PERSON (F_Name, L_Name) STAFF : PERSON (Position, Salary, Manager)
The resulting graph is:
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OODB Schemas: notes OODB schemas capture more semantics than the RDBs.
In particular, an OODB schema: explicitly expresses subsumption relations between
elements; admits special types of arcs for part/whole relationships
in terms of aggregation and composition.
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Semi-structured Data Neither RDBs nor OODBs capture all the features of semi-
structured or unstructured data (Buneman, 1997): semi-structured data do not possess a regular structure
(schemaless); the “structure” of semi-structured data could be partial or
even implicit.
Typical examples are: HTML and XML.
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XML Schemas XML schemas can be represented as DAGs. The graph from the RDB “BANK” could also be obtained
from an XML schema.
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XML Schemas: notes Often XML schemas represent hierarchical data models.
In this case the only relationships between the elements are “is-a”.
Attributes in XML are used to represent extra information about data. There are no strict rules telling us when data should be represented as elements, or as attributes.
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Concept Hierarchies A concept hierarchy is a semi-formal conceptualization of an
application domain in terms of concepts and relationships.
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S-Match: the matching problem Semantic Matching
Given two graphs G and H, for any node ni G and mj H, find
the strongest semantic relation R holding between them The strength of the relations is given by a partial order, that is:
disjointness (), equivalence (≡), more/less specific ( , ), ⊑ ⊒overlap ( ).⊓
A mapping element is a 4-tuple <IDij, ni, mj , R>, where:
IDij is a unique identifier of the given mapping element;
ni is the i-th node of the first graph;
mj is the j-th node of the second graph;
R specifies a semantic relation between the concepts at the given nodes
A mapping is a set of mapping elements19
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Example
< ID22, 2, 2, ≡ >
< ID21, 2, 1, ⊑ >
< ID24, 2, 4, ⊒ >
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Images
Europe
ItalyAustria
2
3 4
1
Italy
Europe
Wine and Cheese
Austria
Pictures
1
2 3
5
⊑
≡
⊒
A mappingA mapping element
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S-Match: the algorithmFour Macro Steps: Given two labeled trees T1 and T2, do:1. For all labels in T1 and T2 compute concepts at labels 2. For all nodes in T1 and T2 compute concepts at nodes3. For all pairs of labels in T1 and T2 compute relations between
concepts at labels4. For all pairs of nodes in T1 and T2 compute relations between
concepts at nodes
Steps 1 and 2 constitute the preprocessing phase (off-line), and are executed once and each time after the schema/ontology is changed(graphs are converted into lightweight ontologies)
Steps 3 and 4 constitute the matching phase (on-line), and are executed every time the two schemas/ontologies are to be matched (the two lightweight ontologies are matched)
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Step 1: compute concepts at labels Natural language expressions are translated into a formal
language Concepts are computed by disambiguating among all possible
senses of words in a label and their interrelations
Computation: Tokenization. Labels are parsed into tokens. Lemmatization. Tokens are morphologically analyzed in order to
find their possible basic forms. Building atomic concepts. An oracle (WordNet) is used to
extract senses of lemmatized tokens. Building complex concepts. Prepositions, conjunctions, etc. are
translated into logical connectives and used to build complex concepts out of the atomic concepts.
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Step 1: compute concepts at labels Tokenization. “Images and text” <Images, and, text>;
Lemmatization. “Images” Image;
Building atomic concepts. “Image” has 8 senses in WordNet, 7 as a noun and 1 as a verb.Some might be filtered out analyzing the context. The rest are kept:“Image” Image#1 ⊔ Image#3 ⊔ Image#7;
Building complex concepts (Image#1 ⊔ Image#3 ⊔ Image#7) ⊔ text#2
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Step 2: compute concepts at nodes Concepts at labels are extended by taking into account the
context of the node, i.e. the position of the node in the tree
Computation: The concept at a node for some node n is computed as the
conjunction of the concepts at labels along the path from the root till the node n itself
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Step 2: compute concepts at nodes
C4 = CEurope ⊓ CPictures ⊓ CItaly
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Italy
Europe
Wine and Cheese
Austria
Pictures
1
2 3
5
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Step 3: compute relations between concepts at labels
Exploit a priori knowledge, e.g., lexical, domain knowledge
with the help of element level semantic matchers
Computation: Concepts at labels of each pair of nodes from the two trees are
compared to determine semantic relations between them (without caring about their context)
The set of semantic relations computed with this step constitute the set of axioms that will be used to compute the mapping, i.e. our TBox!
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Step 3: compute relations between concepts at labels
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Italy
Europe
Wine and
Cheese
Austria
Pictures
1
2 3
4 5
Europe
Italy Austria
2
3 4
1
Images
T1 T2
T2
≡CItaly
≡CAustria
≡CEurope
≡CImages
CAustriaCItalyCPicturesCEuropeT1
CWine CCheese
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Step 4: compute relations between concepts at nodes
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The matching problem is reduced to a set of node matching problems Each node matching problem is reduced to a validity problem
TBox T: the relations between concepts at labels (from step 3) Given the pair of nodes (n, m), deciding if a given semantic relation
holds between them corresponds to verifying that a certain relation holds between corresponding concepts at node: Subsumption: T C⊨ n ⊑ Cm or T C⊨ n ⊒ Cm
Equivalence: T C⊨ n ⊑ Cm and T C⊨ n ⊒ Cm
Disjointness: T C⊨ n C⊓ m ⊑
This is done by eliminating the TBox T and verifying that the negation of each formula is unsatisfiable.
The strongest relation holding between the two nodes is returned
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Step 4: compute relations between concepts at nodes Suppose we want to check if C12 ≡ C22
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T2
=C14
C13
=C12
C11
C25C24C23C22C21T1
(C1Images C2Pictures) (C1Europe C2Europe) (C12 C22 )
Context (the relevant part of the
TBox)
Goal
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The final result
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Italy
Europe
Wine and
Cheese
Austria
Pictures
1
2 3
4 5
Europe
Italy Austria
2
3 4
1Images
T1 T2≡
Italy
Europe
Wine and
Cheese
Austria
Pictures
1
2 3
4 5
Europe
Italy Austria
2
3 4
1Images
T1 T2
Italy
Europe
Wine and
Cheese
Austria
Pictures
1
2 3
4 5
Europe
Italy Austria
2
3 4
1Images
T1 T2
Italy
Europe
Wine and
Cheese
Austria
Pictures
1
2 3
4 5
Europe
Italy Austria
2
3 4
1Images
T1 T2
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A
B E
DJOURNALSjournals#1
C
DEVELOPMENT ANDPROGRAMMING LANGUAGES
(development#1 ⊔ programming#2) ⊓ languages#3 ⊓ journals#1
JAVA(development#1 ⊔ programming#2)
⊓ languages#3 ⊓ journals#1 ⊓ Java#3
PROGRAMMING AND DEVELOPMENTprogramming#2 ⊔ development#1
F
G
LANGUAGESlanguages#3 ⊓(programming#2 ⊔ development#1)
JAVAJava#3 ⊓ languages#3 ⊓(programming#2 ⊔ development#1)
MAGAZINESMagazines#1 Java#3⊓ ⊓ languages#3
⊓ (programming#2 ⊔ development#1)
⊑
⊑
⊑
⊑
⊑
⊑⊑
⊑
⊑
⊒
⊒
≡
It is slow. Can we make the algorithm faster? Too many relations between nodes are returned by S-Match. Are there some relations which are “more important” than others?
Problems with S-Match
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A
B E
D
C F
⊑
⊑
A
B E
D
C F
⊒⊒
A
B E
D
C F
⊥
⊥⊥
A
B E
D
C F
≡ ≡
≡
(1) (2) (3) (4)
⊥
There are some axioms (the dashed arrows) which can be derived from others (the solid ones)
Note that (4) is a combination of (1) and (2) Note that (1) and (2) are still true in case of equivalence
Redundancy patterns
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A redundant mapping element is a mapping element which can be derived from the others using the patterns.
A redundant mapping is a set containing redundant mapping elements
The minimal mapping is the biggest subset of mapping elements among those without redundant elements The minimal mapping always exists and it is unique Advantages in visualization, validation and maintenance
The mapping of maximum size is the set containing the maximum number of mapping elements it can be obtained from the propagation of the elements in the minimal
set using the intuitions encoded in the patterns.
Minimal and redundant mappings
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A
B E
DJOURNALSjournals#1
C
DEVELOPMENT ANDPROGRAMMING LANGUAGES
(development#1 ⊔ programming#2) ⊓ languages#3 ⊓ journals#1
JAVA(development#1 ⊔ programming#2)
⊓ languages#3 ⊓ journals#1 ⊓ Java#3
PROGRAMMING AND DEVELOPMENTprogramming#2 ⊔ development#1
F
G
LANGUAGESlanguages#3 ⊓(programming#2 ⊔ development#1)
JAVAJava#3 ⊓ languages#3 ⊓(programming#2 ⊔ development#1)
MAGAZINESMagazines#1 Java#3⊓ ⊓ languages#3
⊓ (programming#2 ⊔ development#1)
⊑
⊑
⊑
⊑
⊑
⊑⊑
⊑
⊑
⊒
⊒
≡
The minimal mapping
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Computing the minimal mapping M:
function TreeMatch(tree T1, tree T2) {
TreeDisjoint(root(T1),root(T2));
direction := true;
TreeSubsumedBy(root(T1),root(T2));
direction := false;
TreeSubsumedBy(root(T2),root(T1));
TreeEquiv();
};
Computing the set of maximum size:
function Propagate(M)
(3)
(1)
(2)
(4), from (1) and (2)
MinSMatch: the algorithm
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S-Match Lab
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S-MATCH LAB
• Java: JRE or JDK (preferred)• Java IDE: Eclipse, IDEA, NetBeans, …• Text Editor