Finding Semantic Matches Between Conceptual Graphs

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Finding Semantic Matches Between Conceptual Graphs

• University of Texas, Austin
• May 14, 2002

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Talk Outline

• Motivation.
• Matching.
• Rewrite Rules.
• Applications.
• Future Work.
• Related Work.

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Motivation

• Goal Develop a matcher which can determine if
  two concepts are semantically alike.
• Problem Discrepancies in representation. For
  example, the following can be represented in many
  different but equivalent ways.

"John's hand is in a jar filled with cookies."
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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.

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Talk Outline

• Motivation.
• Matching.
• Rewrite Rules.
• Applications.
• Future Work.
• Related Work.

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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.
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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
.
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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.
• Different types of 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.

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Talk Outline

• Motivation.
• Matching.
• Rewrite Rules.
• Applications.
• Future Work.
• Related Work.

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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.

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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.

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Sound Rewrites Transitivity

• Transitivity.
• 21 of our 97 relations are transitive.

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Sound Rewrites Symmetry

• Symmetry.
• 6 of our 97 relations are symmetric.

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Sound Rewrites Part Ascension

• Part Ascension.
• The set S of part-onomic relations is
• is-part-of
• subevent-of
• is-region-of

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Sound Rewrites Covers

• Transitivity and part ascension fit a more
  general pattern that we call the covers rule.

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Sound Rewrites Some More Covers Rule
An excerpt of some of the covers rule from our
rewrite library.
A X in the Trans., Sym., or Reflex. column
indicates the relation is transitive, symmetric,
or reflexive.
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Sound Rewrites Some Statistics on Covers

• 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
r r
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Sound Rewrites Complex Rules

• Sound rewrites can also capture complex
  relationships.
• For example The stop sign is behind the wall,
  which is behind the car, and the car is moving
  away from the wall.

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Sound Rewrites Complex Rules

• The representation of the previous example
• This is an instantiation of the rewrite rule

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Incorporating Rewrites

• With the introduction of rewrites, the matching
  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
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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 The match criterion is exact match.
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An Example Intersection
Intersection of C1 and C2.
The parts of C1 and C2 that match directly are
shown in red, but this does not satisfy the match
criterion. We will align the two concepts with
rewrite rules.
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An Example Transitivity
Apply the transitivity rule for has-part.
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An Example Transitivity
The result of apply the transitivity rule for
has-part.
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An Example Part Ascension
Apply part ascension.
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An Example Part Ascension
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An Example Covers
defeated-by covers caused-by
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An Example Covers
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An Example Match Completed
Intersection of C1 and C2 is not empty and c is
satisfied
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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.
• For example, given the heuristic rule

This is true.
This is not true.
?
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Talk Outline

• Motivation.
• Matching.
• Rewrite Rules.
• Applications.
• Future Work.
• Related Work.

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Applications

• Semantic matching can be applied to a variety of
  applications
• Knowledge Acquisition.
• Rule Bases in general.
• Knowledge-based IR.
• Question Answering.
• Pattern Completion.

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Knowledge Acquisition

• Goal To accelerate a SME's entry of knowledge by
  helping them locate applicable prior knowledge.
• Problem
• Existing KA tools do not reconcile new knowledge
  with existing knowledge.
• They do not identify relevant prior knowledge.
• SME has to be familiar with the KB in order to do
  knowledge entry effectively.
• Semantic matching can be used to locate relevant
  prior knowledge.

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Knowledge-Based IR

• Goal To increase precision in information
  retrieval on digital libraries.
• Problem
• Statistical Methods rely on redundancy and
  co-references in document.
• Existing approaches either do not fully exploit
  the KB or are limited w.r.t. the expressiveness
  of the query (McGuinness, Woods).
• Semantic matching addresses these issues and can
  be applied to this problem.

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Pattern Completion

• Problem Given a user representation, elaborate
  it with a relevant piece of prior knowledge.
• This problem is useful for domains where
  speculation is needed (e.g. Battle Space
  Planning).

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Future Work

• Identify more patterns to populate the library of
  rewrites.
• Identify types of discrepancies in representation
  that rewrites can and cannot handle.
• Identify the boundary of rewrites.
• How to index prior knowledge so search can be
  controlled?
• How best to compose two concepts for elaboration?
• Apply this method to described applications and
  verify utility through experimental studies.

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Related Work

• Conceptual Graphs (Sowa).
• Matching
• Structure mapping and analogy (Forbus, Gentner,
  Markman).
• Using an ontology (McGuinness, Tong, Yu).
• Literal similarity (Tversky).
• Information processing (Les Cohen).
• Graph edits and term graph rewriting (Foggia,
  Bunke, Cook, Holder, Habel, Rozenberg).