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Finding Semantic Matches Between Conceptual Graphs

Finding Semantic Matches Between Conceptual Graphs. Peter Yeh May 14, 2002. Talk Outline. Motivation. Matching. Rewrite Rules. Matching in a KB. Elaboration. Applications. Future Work. Related Work. Motivation.

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Finding Semantic Matches Between Conceptual Graphs

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  1. Finding Semantic Matches Between Conceptual Graphs Peter Yeh May 14, 2002

  2. Talk Outline • Motivation. • Matching. • Rewrite Rules. • Matching in a KB. • Elaboration. • Applications. • Future Work. • Related Work.

  3. Motivation • Goal: Develop a matcher which can determine if two concepts are semantically alike. • Problem: Discrepancies in representation. "John's hand is in a jar filled with cookies."

  4. Motivation • Why: A good semantic matcher has many useful applications • Rule Base: A rule firing requires a match of the consequent or antecedent. • Knowledge Acquisition: Locating relevant pieces of prior knowledge to accelerate knowledge entry. • Knowledge-Based IR: Retrieve information based on semantics. • Pattern Completion: Locate relevant pieces of knowledge to elaborate a user's concept.

  5. Pattern Completion KB User Input

  6. Pattern Completion A piece of prior knowledge from the KB. User Input KB

  7. Pattern Completion The result from elaborating the user’s input

  8. Talk Outline • Motivation. • Matching. • Rewrite Rules. • Matching in a KB. • Elaboration. • Applications. • Future Work. • Related Work.

  9. Matching • Problem: Given two concepts, are they semantically similar? • Formally, Given: C1: A concept. C2: A concept. c: A match criterion. C1 and C2 semantically match iff C1 C2   and c is satisfied.

  10. Matching (cont.) • A part of C1 and C2 intersect iff xx', yy', and rr'. • The general problem is called subgraph morphism in the literature and is NP complete. • We are matching labeled type graphs which is polynomial. However, the matching problem is embedded within other problems. C1 C2 I .

  11. Match Criterion • C1 and C2 intersecting is not enough. The match criterion must also be satisfied. • Match criterion defines what type of match is being performed. • Criterions: • Exact match: C1 is either isomorphic to or a subgraph of C2. • Auto-Classification: The necessary conditions of C1 is a subgraph of C2 and the root of C1 subsumes the root of C2. • Similarity match: The intersection of C1 and C2 is not empty.

  12. Talk Outline • Motivation. • Matching. • Rewrite Rules. • Matching in a KB. • Elaboration. • Applications. • Future Work. • Related Work.

  13. Rewrite Rules • We need rewrite rules to handle discrepancies between two representations of the same piece of information. • Rewrite rules are of the form LHS  RHS. • The LHS and RHS are closely coupled. As a result, a rewrite affects only that part of a concept which is an instantiation of the LHS. • We envision two types of rewrites: • Sound rewrite rules. • Heuristic rewrite rules.

  14. Sound Rewrite Rules • Sound rewrites are universally true. • They are semantics preserving. • They exploit the meta-properties of relations: • transitivity, symmetry, and reflexivity. • part ascension and covers rule. • Our current set of rewrites is not exhaustive. • The methodology we use to populate our library of rewrites is • Identify a pattern. • Exhaustively fill out the pattern with all valid instantiations. • Generalize when possible.

  15. Sound Rewrites: Transitivity • Transitivity. • 21 of our 97 relations are transitive.

  16. Sound Rewrites: Symmetry • Symmetry. • 6 of our 97 relations are symmetric.

  17. Sound Rewrites: Part Ascension • Part Ascension. • The set S of part-onomic relations is: • is-part-of • subevent-of • is-region-of

  18. Sound Rewrites: Covers • Transitivity and part ascension fit a more general pattern that we call the covers rule.

  19. Sound Rewrites: Some More Covers Rule An excerpt of some of the covers rule from our rewrite library.

  20. Sound Rewrites: Some Statistics on Covers r r’ • We have 97 relations in our slot language* • Total number of valid xyz combinations where the range of r and the domain of r’ are the same is 2137. • Total number of valid xyz combinations where y is within the range z is 791. • Total number of covers rule is 210. • Percentages • range of r and domain of r’ the same: 9.8% • y within the range of z: 26.5% r r’

  21. Sound Rewrites: Complex Rules • Sound rewrites can also capture complex relationships. • For example:

  22. Sound Rewrites: Complex Rules • The representation of the previous example • This is an instantiation of the rewrite rule:

  23. Incorporating Rewrites • With the introduction of rewrites, the match problem is redefined as: Given: C1: A concept. C2: A concept. R: A set of rewrites. c: match criterion. C1 and C2 semantically match iff by C1* C1', C1' semantically matches C2 where r R. r

  24. An Example “A Man who blows up a trailer attached to the bumper of a car that he owns, which also has a chassis and a wheel, will cause the car to become detached.” c: Exact match

  25. An Example: Intersection Intersection of C1 and C2.

  26. An Example: Transitivity Applying the Transitivity rule.

  27. An Example: Transitivity

  28. An Example: Part Ascension Applying Part Ascension.

  29. An Example: Part Ascension

  30. An Example: Covers defeated-by covers caused-by

  31. An Example: Covers

  32. An Example: Match Completed Intersection of C1 and C2 is not empty and c is satisfied

  33. Heuristic Rewrite Rules • Heuristic rewrites differ from sound rewrites in only one way. They are not universally true. • Whether or not they hold depends on the semantics of the things involved. • Example: 

  34. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” c: Exact match. “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  35. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” Apply the rule: “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.” 

  36. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” Apply the rule again: “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.” 

  37. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” Assume additional information about the Cable and Pedal was defined. “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  38. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  39. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” Heuristic Rewrite: instrument covers is-part-of “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  40. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  41. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” Heuristic Rewrite: instrument covers has-part “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  42. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  43. Pete’s Rudder Example “The Pilot moved the rudder with the pedal.” Match between the input and the prior “The pilot pressed the pedal which causes the cable to be pull which in turn caused the rudder to move.”

  44. Talk Outline • Motivation. • Matching. • Rewrite Rules. • Matching in a KB. • Elaboration. • Applications. • Future Work. • Related Work.

  45. Matching in a KB • In general, we are given a concept and an existing KB. • Problem: Given a concept, find all the applicable concepts from the KB by applying the match test to each candidate. • Formally, Given: P: Prior Knowledge. I: Given concept. t: A minimum threshold. c: A match criterion. Find: A subset P'  P where for all p  P', p and I semantically match and match-score(I, p) t.

  46. Controlling Search • We must look through the KB to find the relevant concepts. • This is very expensive. • Possible Solution: Index the prior knowledge in some fashion so the entire KB does not need to be examined (work in progress). • SMEs can help by: • selecting the most relevant piece of knowledge from a set of matches. • picking a starting point to search from. • providing a set of candidates to match.

  47. Talk Outline • Motivation. • Matching. • Rewrite Rules. • Matching in a KB. • Elaboration. • Applications. • Future Work. • Related Work.

  48. Elaboration • Problem: Given a user concept and a relevant prior, how can the two be overlaid s.t. the prior meaningfully elaborates the user concept. • More specifically, • We're aiming for a semi-automated approach to elaboration where the system suggests I' and the user can accept or modify I'. Given: I: user graph p: An applicable prior knowledge Generate: A new graph I' = I ° p.

  49. An Example of Elaboration p: Description of Bioremediation entered by a SME. I: Definition of Conversion from the KB.

  50. An Example of Elaboration I’ = I ° p Initial composition of bioremediation and conversion.

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