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Semantic Matching. Fausto Giunchiglia. work in collaboration with Pavel Shvaiko . The Italian - Israel i F orum on Computer Science, Haifa , J une 17-18, 2003. Matching Syntactic Matching Semantic Matching On Implementing Semantic Matching Conclusions. Outline. MATCHING.
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Semantic Matching Fausto Giunchiglia work in collaboration with Pavel Shvaiko The Italian-IsraeliForum on ComputerScience, Haifa,June 17-18, 2003
Matching Syntactic Matching Semantic Matching On Implementing Semantic Matching Conclusions Outline
Generic Model Management Schema integration Data warehouses E-commerce Semantic query processing Data Coordination in P2P systems Application Domains
RDB Schemas OODB Schemas XML Schemas Concept Hierarchies Ontologies Matching Problems
www.google.com www.yahoo.com Arts Arts&Humanities Art History Art History Music Sr={} Design Art Organizations Organizations Sc=1.0 Architecture History Sr={} History Sr={} Baroque Baroque Sc=1.0 Example of Matching
Match is an operator that takes two graph-like structures (e.g., database schemas or ontologies) and produces a mapping between elements of the two graphs that correspond semantically to each other Matching
The problem of matching can be decomposed in two steps: Extract graphs from the data and conceptual models Match the resulting graphs (generic matching) Matching
Mapping element is a 4-tuple < mID, Ni1, Nj2, R >, i=1...h; j=1..k; where mID is a unique identifier of the given mapping element; Ni1 is the i-th node of the first graph, h is the number of nodes in the first graph; Nj2is the j-th node of the second graph, k is the number of nodes in the second graph R specifies a similarity relation of the given nodes Mappingis a set of mapping elements Matching is the process of discovering mappings between two graphs through the application of a matching algorithm Matching
Matching Syntactic Matching Semantic Matching Matching: Syntactic AND Semantic • R is computed between concepts at nodes • R = {set-theoretic relations, e.g., =, , , , } • R is computed between labels at nodes • R = [0,1]
Mapping element is a 4-tuple < mID, Li1, Lj2, R >, where Li1 is the label at the i-th node of the first graph; Lj2is the label at the j-th node of the second graph; R specifies a similarity relation in the form of a coefficient, which measures the similarity between the labels of the given nodes Example: R is a similaritycoefficient in [0,1] R= <m21,telephone, phone,0.7> Syntactic Matching
www.google.com www.yahoo.com Arts Arts&Humanities Art History Art History Sc=1.0 Music Design Art Sc=0.7 Organizations Organizations Sc=0.9 Sc=1.0 Architecture History Sc=1.0 History Sc=0.7 Sc=0.7 Baroque Baroque Sc=1.0 (final result) Example: Cupid (tentative links)
Cupid … is a hybrid matching prototype. It exploits linguistic and structural schema matching heuristics, and computes similarity coefficients between nodes of the trees. Similarity Flooding … is a hybrid matching prototype. It uses fix-point computation to determine correspondences between nodes of the graphs. COMA …is a composite matching prototype. It provides an extensible library of different matchers which manipulate DAGs and supports various ways of combining final results. As far as we know, so far only syntactic matching… The State of the Art
Mapping elementis a 4-tuple < mID, Ci1, Cj2, R >, where Ci1 is the concept of the i-th node of the first graph; Cj2is the concept of the j-th node of the second graph; R specifies a similarity relation in the form of a semantic relation between the extensions of concepts at the given nodes Possible R’s: equality {=}, overlapping {}, mismatch {}, more general/specific {, } Example:R= <m21,telephone, phone,{=}> Semantic Matching
Examples: Analysis of Siblings • Suppose that we want to match nodes 51 and 22 • Cupid:R = 0,8. This is because A1=A2,C1=C2 and we have the same structures on both sides (no importance of order of links) • A semantic matching approach compares concepts A1C1 with A2C2andproduces C51 = C22
Examples: Analysis of Ancestors. Case 1 • Suppose that we want to match nodes 51 and 12 • Cupid does not find a similarity coefficient between the nodes under consideration, due to the significant differences in structure of the given graphs • Semantic matching: The concept denoted by the label at node 51 is C1, while the concept at node 51is C51 = A1C1. The concept at node 12isC12= C2. Thus, C51 C12
Examples: Analysis of Ancestors. Case 2 • Suppose that we want to match nodes 51 and 52 • Cupid:R= 0,86. This is because of the identity of labels A1=A2,C1=C2 • Semantic matching: The concept at node 51 is C51= A1C1; while the concept at node 52is C52=A2*C2. Since we have that A1=A2and C1=C2, then C52 C51
Examples: Enriched Analysis of Siblings • Suppose that we want to match nodes 21 and 22 • Cupid:R= 0,68. This is mainly because of the entry in the thesaurus specifying Belgiumasa part of Benelux, and due to the fact that the nodes with labels Benelux1 andBelgium2 are leaves • Semantic matching: We treat C21as Benelux1Netherlands1 Luxembourg1 = Belgium. Thus, C21 = C22
ON IMPLEMENTING SEMANTIC MATCHING
Semantic Matching Element - level Structure - level On Implementation Weak Semantics Techniques Strong Semantics Techniques
Weak Semantics Techniques Analysis of strings {=} <phone, telephone,{=}> Analysis of data types {=, , , , } <string, integer,{}> <integer, real,{}> Analysis of soundex {=} < Fausto, Phausto,{=}> Strong Semantics Techniques Precompiled thesaurus syn key <Discount, Rebate,{=}> WordNet <Art_#1, Humanities_#1,{}>, where #1 … sense number 1 of the word Art according to WordNet Element-level Semantic Matching
Semantic Relations via WordNet Equality: one concept is equal to another if there is at least one sense of the first concept, which is a synonym of the second Overlapping: one concept is overlapped with the other if there are some senses in common Mismatch: two concepts are mismatched if they have no sense in common More general: one concept is more general then the other iff there exists at least one sense of the first concept that has a sense of the other as a hyponym or meronym Less general: one concept is less general than the other iff there exists at least one sense of the first concept that has a sense of the other concept as hypernym or as a holonym Element-level Semantic Matching (cont.)
We translate the matching problem, namely the two graphs (in particular, the pair of nodes submitted to matching) into a propositional formula and then check for its validity We check for validity using SAT Structure-level Semantic Matching
Extract the two graphs Compute element-level semantic matching Compute concepts at nodes Construct the propositional formula Run SAT Perform iterations Semantic Matching Algorithm
Extract the two graphs Semantic Matching Algorithm: Example – (1) • In the case of RDB, XML and OODB schemas, it is necessary to extract useful semantic information, for instance in the form of ontologies
Element-level semantic matching.For each node, compute semantic relations holding among all the concepts denoted by labels at nodes under consideration • A1 =A2 • B1 = B2 • C1 =C2 • D1 = D2 • E1 =E2 Semantic Matching Algorithm: Example – (2)
Compute concepts at nodes.Suppose, we want to find a semantic relation between nodes 51 and 12 ? Semantic Matching Algorithm: Example – (3) • C11 =A1 • C51 =A1 C2 • C12 =C2 • C51C12
Construct the propositional formula. We translate all the semantic relations computed in step 2 into propositional formulas under the following rules: ? Semantic Matching Algorithm: Example – (4) • A1 A2A2 A1 • A1 A2A1 A2 • A1 = A2A1 A2 • A1 A2(A1 A2) • From step 2 we have: C1C2 • We want to prove that C51C12 ( we guess relation between nodes at this stage) • (A1C1)C2 • (C1C2) ((A1C1)C2)
Run SAT In order to prove that (C1C2) ((A1C1 )C2)is valid, we prove that its negation is unsatisfiabile (C1C2) ((A1C1)C2) SAT returns FALSE Thus, C51C12 Semantic Matching Algorithm: Example – (5)
Iterations. Iterations are performed re-running SAT Semantic Matching Algorithm: Example – (6.1) • Suppose, that C21 C22 • …an oracle tells us that A1 = F2 G2 • After this additional analysis we can infer C21= C22
Iterations. …to use the result of a previous match Semantic Matching Algorithm: Example – (6.2) • Suppose, that F1B2 • Having found thatC41C42 • We can automatically infer thatC51C52
www.google.com www.yahoo.com {} Arts Arts&Humanities Art History Art History Music {} {} Design Art Organizations Organizations Architecture History {} {} History {} Baroque Baroque Example: Cupid vs. Semantic Matching
We have made a rational reconstruction of the major matching problems and articulated them in terms of the more generic problem of matching graphs We have identified semantic matching as a new approach for performing generic matching We have proposed an implementation of semantic matching using SAT Conclusions
Extend to a full graph matcher How to extract semantics from schemas Study how to take into account attributes and instances Develop an efficient implementation of the system Do a thorough testing of the system Future Work
Project website: http://www.dit.unitn.it/~p2p/ F. Giunchiglia, P.Shvaiko “Semantic Matching”. Technical Report #DIT-03-013, Trento, 2003. Also to appear in Proc. of ODS at IJCAI – 03. F. Giunchiglia, I. Zaihrayeu “Making peer databases interact – a vision for an architecture supporting data coordination” In Proc. Of the Conference of Information Agents (CIA 2002), Madrid, 2002 References