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Semantic Matching

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

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  1. Semantic Matching Fausto Giunchiglia work in collaboration with Pavel Shvaiko The Italian-IsraeliForum on ComputerScience, Haifa,June 17-18, 2003

  2. Matching Syntactic Matching Semantic Matching On Implementing Semantic Matching Conclusions Outline

  3. MATCHING

  4. Generic Model Management Schema integration Data warehouses E-commerce Semantic query processing Data Coordination in P2P systems Application Domains

  5. RDB Schemas OODB Schemas XML Schemas Concept Hierarchies Ontologies Matching Problems

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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]

  11. SYNTACTIC MATCHING

  12. 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

  13. 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)

  14. 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

  15. SEMANTIC MATCHING

  16. 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

  17. 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 A1C1 with A2C2andproduces C51 = C22

  18. 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 C1, while the concept at node 51is C51 = A1C1. The concept at node 12isC12= C2. Thus, C51 C12

  19. 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= A1C1; while the concept at node 52is C52=A2*C2. Since we have that A1=A2and C1=C2, then C52 C51

  20. 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 Benelux1Netherlands1 Luxembourg1 = Belgium. Thus, C21 = C22

  21. ON IMPLEMENTING SEMANTIC MATCHING

  22. Semantic Matching Element - level Structure - level On Implementation Weak Semantics Techniques Strong Semantics Techniques

  23. 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

  24. 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.)

  25. 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

  26. Extract the two graphs Compute element-level semantic matching Compute concepts at nodes Construct the propositional formula Run SAT Perform iterations Semantic Matching Algorithm

  27. 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

  28. Element-level semantic matching.For each node, compute semantic relations holding among all the concepts denoted by labels at nodes under consideration • A1 =A2 • B1 = B2 • C1 =C2 • D1 = D2 • E1 =E2 Semantic Matching Algorithm: Example – (2)

  29. Compute concepts at nodes.Suppose, we want to find a semantic relation between nodes 51 and 12 ? Semantic Matching Algorithm: Example – (3) • C11 =A1 • C51 =A1 C2 • C12 =C2 • C51C12

  30. 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) • A1 A2A2 A1 • A1 A2A1 A2 • A1 = A2A1 A2 • A1 A2(A1 A2) • From step 2 we have: C1C2 • We want to prove that C51C12 ( we guess relation between nodes at this stage) • (A1C1)C2 • (C1C2)  ((A1C1)C2)

  31. Run SAT In order to prove that (C1C2)  ((A1C1 )C2)is valid, we prove that its negation is unsatisfiabile (C1C2)  ((A1C1)C2) SAT returns FALSE Thus, C51C12 Semantic Matching Algorithm: Example – (5)

  32. Iterations. Iterations are performed re-running SAT Semantic Matching Algorithm: Example – (6.1) • Suppose, that C21 C22   • …an oracle tells us that A1 = F2  G2 • After this additional analysis we can infer C21= C22

  33. Iterations. …to use the result of a previous match Semantic Matching Algorithm: Example – (6.2) • Suppose, that F1B2 • Having found thatC41C42 • We can automatically infer thatC51C52

  34. 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

  35. 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

  36. 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

  37. 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

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