1. Logics for Data and Knowledge Representation
Semantic Matching

2. Outline Introduction: Kinds of matching: Syntactic versus Semantic
Why matching?
The matching problem
Kinds of matching: Syntactic versus Semantic
Steps in matching
Kinds of schemas
S-Match
MinSMatch

3. Approaching the heterogeneity problem
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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.
From paper:
Giunchiglia, Fausto and Soergel, Dagobert and Maltese, Vincenzo and Bertacco, Alessandro. Mapping large-scale Knowledge Organization Systems. Proc. of the 2nd International Conference on the Semantic Web and Digital Libraries (ICSD), 2009. 3 3

4. The Matching Problem
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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. 4

5. A Matching Problem
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH ? 5

6. Kinds of Matching: Syntactic versus Semantic (I)
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
Syntactic matching
Matching of nodes as objects or strings (without meaning)
“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

7. Kinds of Matching: Syntactic versus Semantic (II)
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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.
Semantic matching
Relations 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. 7

8. Steps in matching A matching problem can be decomposed in three steps:
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
A matching problem can be decomposed in three steps:
Extract the graphs from the conceptual models under consideration;
Convert the graphs into formal ontologies
Match the formal ontologies
In the next slides we show some examples of step 1
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

9. Relational DB Schemas
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
Let us consider the following relational database (RDB) model, say “BANK”:
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.
We can represent the RDB model “BANK” as a graph (i.e. a tree) with root “BANK”.

10. Relational DB Schemas: Representation #1
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
The RDB model is first partitioned into relations, then attributes and data instances.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

11. Relational DB Schemas: Representation #2
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
The model is partitioned into relations, then into tuples, attributes and data instances.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

12. Relational DB Schemas: notes
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

13. OODB Schemas
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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:
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

14. OODB Schemas: notes OODB schemas capture more semantics than the RDBs.
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

15. Semi-structured Data
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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.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

16. XML Schemas XML schemas can be represented as DAGs.
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
XML schemas can be represented as DAGs.
The graph from the RDB “BANK” could also be obtained from an XML schema.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

17. XML Schemas: notes
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

18. Concept Hierarchies
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
A concept hierarchy is a semi-formal conceptualization of an application domain in terms of concepts and relationships.
From paper:
SEMANTIC MATCHING Fausto Giunchiglia and Pavel Shvaiko
April Technical Report # DIT
Also in : Knowledge Engineering Review, 18(3):265–280, 2003.

19. S-Match: the matching problem
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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 elements 19

20. Example ⊑ ≡ ⊒ < ID22, 2, 2, ≡ > < ID21, 2, 1, ⊑ >
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH 4
Images
Europe
Italy
Austria 2 3 1
Wine and Cheese
Pictures 5 ⊑ ≡ ⊒
< ID22, 2, 2, ≡ >
< ID21, 2, 1, ⊑ >
< ID24, 2, 4, ⊒ >
A mapping
A mapping element 20

21. S-Match: the algorithm
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
Four Macro Steps: Given two labeled trees T1 and T2, do:
For all labels in T1 and T2 compute concepts at labels
For all nodes in T1 and T2 compute concepts at nodes
For all pairs of labels in T1 and T2 compute relations between concepts at labels
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) 21

22. Step 1: compute concepts at labels
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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. 22

23. Step 1: compute concepts at labels
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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 23

24. Step 2: compute concepts at nodes
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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 24

25. Step 2: compute concepts at nodes
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH 4
Italy
Europe
Wine and Cheese
Austria
Pictures 1 2 3 5
C4 = CEurope ⊓ CPictures ⊓ CItaly 25

26. Step 3: compute relations between concepts at labels
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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! 26

27. Step 3: compute relations between concepts at labels
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
Italy
Europe
Wine and
Cheese
Austria
Pictures 1 2 3 4 5
Images T1 T2 T2  ≡
CItaly
CAustria
CEurope
CImages
CPictures T1
CWine
CCheese 27

28. Step 4: compute relations between concepts at nodes
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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 ⊨ Cn ⊑ Cm or T ⊨ Cn ⊒ Cm
Equivalence: T ⊨ Cn ⊑ Cm and T ⊨ Cn ⊒ Cm
Disjointness: T ⊨ Cn ⊓ Cm ⊑ 
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

29. Step 4: compute relations between concepts at nodes
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
Suppose we want to check if C12 ≡ C22
(C1Images  C2Pictures)  (C1Europe  C2Europe)  (C12  C22 )
Goal
Context
(the relevant part of the TBox) T2  =
C14
C13
C12
C11
C25
C24
C23
C22
C21 T1

30. ≡  The final result T1 T2 T1 T2 T1 T2 T1 T2 Italy Europe Wine and
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH ≡
Italy
Europe
Wine and
Cheese
Austria
Pictures 1 2 3 4 5
Images T1 T2
Italy
Europe
Wine and
Cheese
Austria
Pictures 1 2 3 4 5
Images T1 T2 
Italy
Europe
Wine and
Cheese
Austria
Pictures 1 2 3 4 5
Images T1 T2
Italy
Europe
Wine and
Cheese
Austria
Pictures 1 2 3 4 5
Images T1 T2

31. Problems with S-Match It is slow. Can we make the algorithm faster?
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
JOURNALS
journals#1 A ⊑ D
PROGRAMMING AND DEVELOPMENT
programming#2 ⊔ development#1 ⊒ ⊑ ⊑ ⊑
DEVELOPMENT AND
PROGRAMMING LANGUAGES
(development#1 ⊔ programming#2)
⊓ languages#3 ⊓ journals#1 ⊑
LANGUAGES
languages#3 ⊓
(programming#2 ⊔ development#1) B E ⊒ ⊑ ⊑ ⊑
JAVA
(development#1 ⊔ programming#2)
⊓ languages#3 ⊓ journals#1
⊓ Java#3 C F
JAVA
Java#3 ⊓ languages#3 ⊓
(programming#2 ⊔ development#1) ⊑ ≡ G
MAGAZINES
Magazines#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? 31 31

32. Redundancy patterns
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH 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 32 32

33. Minimal and redundant mappings
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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. 33 33

34. The minimal mapping A ⊑ D ⊒ ⊑ ⊑ ⊑ ⊑ B E ⊒ ⊑ ⊑ ⊑ C F ⊑ ≡ G 34 JOURNALS
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
JOURNALS
journals#1 A ⊑ D
PROGRAMMING AND DEVELOPMENT
programming#2 ⊔ development#1 ⊒ ⊑ ⊑ ⊑
DEVELOPMENT AND
PROGRAMMING LANGUAGES
(development#1 ⊔ programming#2)
⊓ languages#3 ⊓ journals#1 ⊑
LANGUAGES
languages#3 ⊓
(programming#2 ⊔ development#1) B E ⊒ ⊑ ⊑ ⊑
JAVA
(development#1 ⊔ programming#2)
⊓ languages#3 ⊓ journals#1
⊓ Java#3 C F
JAVA
Java#3 ⊓ languages#3 ⊓
(programming#2 ⊔ development#1) ⊑ ≡ G
MAGAZINES
Magazines#1 ⊓ Java#3 ⊓ languages#3
⊓ (programming#2 ⊔ development#1) 34 34

35. MinSMatch: the algorithm
INTRODUCTION :: KINDS OF MATCHING :: STEPS :: KINDS OF SCHEMAS :: S-MATCH :: MINSMATCH
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) 35 35