Guiding Inference with Conceptual Graphs Bruce Porter Univ Texas at Austin Peter Clark Boeing...

Guiding Inference with Conceptual Graphs

Bruce Porter

Univ Texas at Austin

Peter Clark

Boeing Research

Context: Multifunctional KBs

• Goal: KB can answer a wide variety of questions

• Need representation language which

– is natural for the K engineer (CGs)

– supports inference (CGs?)

• Botany KB:

– 20k concepts (“graphs”), 100k facts

– CG-like language = KM

Vocabularies for Inference• Beta rules: the “assembly code” of

inference• Minimal joins: a “derived rule”

P:p1

schema for P(x) isP:*x r Q

r QP:p1=

+

(a `scenario’)

(a schema)

(an elaborated scenario)

Minimal join = a sequence of beta rulesP:p1

schema for P(x) isP:*x r Q r QP:p1+ =

P:p1 P:*x r(P:*x,Q)

P:p1 P:*x r(P:*x,Q)P:p1

P:p1 r(P:p1,Q)P:p1

P:p1 r(P:p1,Q)

P:p1 r(P:p1,Q)

r QP:p1=

(insertion)

(coreferent join)

(deiteration)

(double negation)

QED

Proof:

The CG Inference Task• Given:

– an initial scenario CG– a query (= unknown node in the scenario)

• Find:– a sequence of joins which instantiate that node

(answer the query)

objperson:joe necktieagnt buy:b01

buy:b01

inst

?

Scenario:

Query:

Goal: find ?

(“what is the instrument of the buy?” Ans: $10)

Inference using Joins

objperson:joe necktiebuy:b01agnt

inst

?

Query: inst(b1,X)?Query: “What is the instrument of the buy?” (Ans: $10)

objperson physobjbuy:*xagnt

inst

money:@?

valueposs

schema for buy(x) is

inst

money:@?

valueposs

necktie:*x

value

schema for necktie(x) is

$10

worn-by

person

money:$10

worn-by

person

Ans: $10!

An alternative sequence of joins


inst

?

Query: inst(b1,X)?


inst

money:@?

valueposs


inst

money:@?

valueposs

person:*x

part

head

part

body

schema for person(x) is

part

head

part

body

schema for head(x) is

head has hair

shaperound

has hair

shaperound

money:*x carry-in wallet

schema for money(x) is

carry-in wallet

Solution: Access Paths• A chain of predicates (path in a CG)• Encodes how to compute a node from others

– 1. follow the path– 2. if stuck, do a join at the current node

• Introduces controlled incompleteness

The Inference Problem

• Many joins possible• Complete reasoning is intractible!

Schema with Access Paths


inst

*x.obj.value

poss

*x.inst


Standard CG Schemaobjperson physobjbuy:*xagnt

inst

money:@?

valueposs


value

?

Query: inst(b1,X)?


Query: “What is the instrument of the buy?” (Ans: $10)

Example of paths guiding inference

?

inst


objperson physobjbuy:*bagnt

inst

*b.obj.value

poss

*b.inst

inst

b1.obj.value

inst

b1.obj.value

value

?

Query: inst(b1,X)?


Query: “What is the instrument of the buy?” (Ans: $10)

Example of paths guiding inference

inst

b1.obj.value

value

?

necktie:*x

value

$10

person

worn-byschema for necktie(x) is

value

$10

Ans: $10!

Inference with Access Paths

• Algorithm:

– follow the path

– if stuck, do a join at current node

• Provides a focal point in the graph

• Defines when and where to expand

• Focuses/restricts inference

Adding Type Definitions

• Type definitions allow classification

• => class of objects in scenario may need updating

• Requires a classification step after each join

adhesive:a1 joins wood

type nail(x) is adhesive:*x joins wood

nail:a1 joins wood

(scenario)

(type defn)

(elaborated scenario)

+

=

assemble:a1objtable

Query: inst(a1,X)?Query: “What instrument assembles a table?” (Answer: “a hammer”)

inst

?

assemble:*xobjphysobj inst

*x.adhesive.tool

adhesive

adhesivejoins*x.obj.matr

schema for assemble(x) is

inst

a1.adhesive.tool

assemble:a1objtable


inst

?inst

a1.adhesive.tool

?

adhesive

? tool


*x.adhesive.tool

adhesive



adhesive

adhesive

assemble:a1objtable


inst

?inst

a1.adhesive.tool

?

adhesive

? tool

adhesive

adhesivenail

hammer

metal

made-of

toolnail:*xjoinswood

schema for nail(x) is

hammertool

Ans: hammer!

assemble:a1objtable


inst

?inst

a1.adhesive.tool

?

adhesive

? tool

adhesive

adhesive

adhesive:*xjoinswood

type nail(x) is

Subquery: joins(adh1,wood)?

joins?

assemble:a1objtable


inst

?inst

a1.adhesive.tool

?

adhesive

? tool

adhesive

adhesive


joins?


*x.adhesive.tool

adhesive



joinsa1.obj.matr

assemble:a1objtable


inst

?inst

a1.adhesive.tool

?

adhesive

? tool

adhesive

adhesive


joins? joinsa1.obj.matr

matr

?

table:*x

matr

wood

schema for table(x) is

legs

4

purpose support

matr

wood

matr

wood

assemble:a1objtable


inst

?inst

a1.adhesive.tool

?

adhesive

? tool

adhesive

adhesive

Subquery: joins(adh1,wood)!

joins? joinsa1.obj.matr

adhesive:*xjoinswood

type nail(x) is

nail

matr

wood

assemble:a1objtable


inst

?inst

a1.adhesive.tool

?

adhesive

? tool

adhesive

adhesivejoins? joinsa1.obj.matrnail

Discussion

• Paths

– specify preferred sequence of subgoals

– say which joins to perform

• Restricts and focuses inference

• Trade-off completeness for tractability

• Key issue: Can engineer encode suitable paths?

• Extension of CGs

Summary

• Inference with CGs: beta rules and joins

• Search problem: which sequence of joins to use?

• Soln: access paths

– focus inference

– show where and when to do a join

• Basis for the Botany KB (Univ Texas Austin) + some of Boeing’s new KR work

Guiding Inference with Conceptual Graphs Bruce Porter Univ Texas at Austin Peter Clark Boeing...

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