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• 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."

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.

Pattern Completion

User Input

KB

Pattern Completion

User Input

A piece of prior knowledge from

the KB.

KB

Pattern Completion

The result from elaborating the user’s input

Talk Outline

• Motivation.

• Matching.

• Rewrite Rules.

• Matching in a KB.

• Elaboration.

• 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.

• 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.

• Matching in a KB.

• Elaboration.

• 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. covers

causes(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.

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:

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 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

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

An Example: Intersection

Intersection of C1 and C2.

An Example: Transitivity

Applying the Transitivity rule.

An Example: Transitivity

An Example: Part Ascension

Applying 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.

• Example:

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.”

c: Exact match.

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.”

Apply the rule:

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.”

Apply the rule again:

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.”

Assume additional information about the Cable and Pedal was defined.

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.”

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.”

Heuristic Rewrite: instrument covers is-part-of

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.”

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.”

Heuristic Rewrite: instrument covers has-part

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.”

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.”

Match between the input and the prior

Talk Outline

• Motivation.

• Matching.

• Rewrite Rules.

• Matching in a KB.

• Elaboration.

• Applications.

• Future Work.

• Related Work.

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.

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.

Talk Outline

• Motivation.

• Matching.

• Rewrite Rules.

• Matching in a KB.

• Elaboration.

• Applications.

• Future Work.

• Related Work.

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.

An Example of Elaboration

I:

p:

Definition of Conversion from the KB.

Description of Bioremediation entered by a SME.

An Example of Elaboration

I’ = I ° p

Initial composition of bioremediation and conversion.

An Example of Elaboration

I’ = I ° p

Talk Outline

• Motivation.

• Matching.

• Rewrite Rules.

• Matching in a KB.

• Elaboration.

• 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 (Shaken).

– 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).

An Example of Pattern Completion

I:

p:

c: Exact match.

Definition of Vertical-Envelopment from the KB.

SME: What is the larger context of this particular

landing?

Pattern Completion: Definition Expansion

I:

Expand the definition of Flight

p:

Pattern Completion: Transitivity

I:p:

Apply the transitivity rule.

Pattern Completion: Transitivity

I: p:

Result of applying the transitivity rule.

Pattern Completion: Rewrite Rule

Apply the rewrite:

Must first apply preparatory-event-of covers subevent to align LHS.

I:

p:

Pattern Completion: Rewrite Rule

I: p:

The result of applying the previous rewrite.

Pattern Completion: Covers and Heuristic Rule.

- Apply is-near covers location-of.

- Apply the heuristic rewrite that

I:

p:

allows siblings to match.

Pattern Completion

Intersect of I and p with c also being satisfied.

I:p:

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).

– Literal Similarity (Tversky).

– Information Processing (Les Cohen).

– Graph Isomorphism.

– Subgraph morphism.

• Graph Transformations.