Finding Semantic Matches Between Conceptual Graphs

Finding Semantic Matches Between Conceptual Graphs

University of Texas, AustinMay 14, 2002

Talk Outline

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

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."

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.

Talk Outline

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

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.

Matching (cont.)• A part of C1 and C2 intersect iff xx', yy', and rr'.

• 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.

I

.

C1 C2

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.

Talk Outline

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

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.

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.

Sound Rewrites: Transitivity

• Transitivity.• 21 of our 97

relations are transitive.

Sound Rewrites: Symmetry

• Symmetry.• 6 of our 97

relations are symmetric.

Sound Rewrites: Part Ascension

• Part Ascension. • The set S of part-

onomic relations is:– is-part-of– subevent-of– is-region-of

Sound Rewrites: Covers

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

Sound Rewrites: Some More Covers Rule

relation Trans. Sym. Reflex. coverscauses

(caused-by) X - -subevent, resulting-state

(subevent-of, resulting-from)

defeats(defeated-by) - - - (caused-by, subevent-of)

enables(enabled-by) X - -

causes, resulting-state, subevent(caused-by, resulting-from,

subevent-of)entails

(entailed-by) X - -causes, resulting-state, subevent

(caused-by, resulting-from,subevent-of)

inhibits(inhibited-by) - - -

resulting-state, subevent-of(caused-by, resulting-from,

subevent-of)by-means-of

(means-by-which) X - - -

prevents(prevented-by) - - -

subevent-of(subevent-of, caused-by,

resulting-from)

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.

Sound Rewrites: Some Statistics on Covers

• We have 97 relations in our slot language*

• Total number of valid xyz combinations where the range of r and the domain of r’ are the same is 2137.

• Total number of valid xyz 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’

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.”

Sound Rewrites: Complex Rules

• The representation of the previous example

• This is an instantiation of the rewrite rule:

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

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.

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.

An Example: Transitivity

Apply the transitivity rule for has-part.

An Example: Transitivity

The result of apply the transitivity rule for has-part.

An Example: Part Ascension

Apply part ascension.

An Example: Part Ascension

An Example: Covers

defeated-by covers

caused-by

An Example: Covers

An Example: Match Completed

Intersection of C1 and C2 is not empty and c is satisfied

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.

Talk Outline

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

Applications

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

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.

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.

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).

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.

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).