CS 544: Lecture 3.4Interpretation as Abduction

and Local Pragmatics

Jerry R. Hobbs

USC/ISI

Marina del Rey, CA

Logical Form

The logical form of a sentence (or text) is an existentially quantified conjunction of positive ground literals. (Existential quantification is over a Platonic universe of possible individuals, including eventualities and typical elements.)

John didn't work again. ==>

(E j, e1, e2, e3, e4, e5) Rexists(e5) & again'(e5,e3) & not'(e3,e2) & past'(e2,e4) & work'(e4,j) & John'(e1,j)

OR

again(e3) & not'(e3,e2) & past'(e2,e4) & work'(e4,j) & John(j)

Outline

Abduction

Solutions to Local Pragmatics Problems using Abduction

How Weighted Abduction Works

Some Systems Using Abduction

Interpreting the Environment:Abduction

Boat in Tree by Sea

Storm

ExplainEntities in

Environment

cause

Explain Relationsin Environment

Interpreting the Environment:Picking the Best Explanation

boat in tree tree down

crane chopped down

storm

?

Interpreting the Environment:Picking the Best Explanation

boat in tree tree down

crane chopped down

storm

in magazine

ad agency

advertisement

Interpreting the Environment

observable-1 observable-2 observable-3

underlyingcause

underlyingcause

deeperunderlying

cause

In Abduction,best explanationcan be variable depth.

What is Abduction?

Deduction: p(a), (A x) p(x) --> q(x) ==> q(a)

Induction: p(a), q(a) ==> (A x) p(x) --> q(x)

Abduction: q(a), (A x) p(x) --> q(x) ==> p(a)

Abduction = Deduction + Assumptions + Cost function on proofs

Interpretation as Abduction

To Interpret a Situation: Find the best explanation for the observables.

Abduction: Inference to the best explanation.

1. Represent the observables as propositions.

2. Prove them, using the axioms in the knowledge base.

3. Allow assumptions in the proof, at a cost.

4. Pick the cheapest proof: Shortest proof Fewest and most plausible assumptions Greatest redundancy Most salient axioms

Cognitive Benefit

Knowledge of causal and implicationalstructure of current situation

Ability to manipulate causal and implicational structure of situation

to achieve goals

Interpreting Discourse

An utterance presents "observable" propositions.

To interpret an utterance, find the best explanation for the propositional content of the utterance.

1. Represent the content as propositions (the logical form). 2. Prove them, using the axioms in the knowledge base.3. Allow assumptions in the proof, at a cost.4. Pick the cheapest proof: Shortest proof Fewest and most plausible assumptions Greatest redundancy Most salient axioms

Interpretation as Abduction

1. Represent the content as predications (the logical form). 2. Prove them, using the axioms in the knowledge base.3. Allow assumptions in the proof, at a cost.4. Pick the lowest cost proof.

HearerSpeaker MB

Utt

Uniform frameworkfor syntax, semantics,and pragmatics

Factors in Cost

1. Salience of Facts and Axioms Used in Proof

2. Size of Proof

3. Number and Plausibility of Assumptions

4. Use of Redundant Information in Proofs

Knowledge Base / Belief System

Expressed as large collection of (defeasible) axioms of form:

( x,z) p1(x) & p2(x,z) --> ( y) q1(y,x) & q2(y) e.g., jar(y) --> container(y,x) & fluid(x) (A jar is a container for fluid)

car(x) --> engine(y,x) (Cars have engines)

fly'(e1,x,y) --> move-fast'(e,x,y) & imply(e1,e) (Flying implies moving fast)

Nonmonotonicity or Defeasibility

bird(x)w1 & etc1(x)w2 --> fly(x)

You can never prove this, but you can assume it for a cost.This may yield lowest cost interpretation.

mammal(x)w3 & etc2(x)w4 <--> elephant(x)

genus differentiae species

Outline

Abduction

Solutions to Local Pragmatics Problems using Abduction

How Weighted Abduction Works

Some Systems Using Abduction

Example

The Boston office called.

Local Pragmatics Problems illustrated:

1. Definite Reference: What does the Boston office refer to?

2. Interpreting compound nominals: What is the implicit relation between Boston and office?

3. Metonymy: Coerce from the Boston office to someone at the Boston office.

The Example Interpreted The Boston office called.

LF: call'(e,x) & person(x) & rel(x,y) & office(y) & Boston(z) & nn(z,y)KB: person(J)

work-for(J,O), office(O)

work-for(x,y) --> rel(x,y)

in(O,B), Boston(B)

in(y,z) --> nn(z,y)

Syntax : Parse Tree :: Interpretation : Proof Graph

New Information

DefiniteReference

Metonymy

Compound Nominal

“Local Pragmatics” problems solved as a by-product

Definite Reference John bought a new car. The engine is already broken.

LF: . . . & car(c) & . . . . . . & engine(y,x) & . . .

KB: car(x) --> engine(y,x)

Definite Reference with Implicature:

John walked into the room. The chandelier shone brightly.

LF: . . . & room(r) & . . . . . . & chandelier(y) & . . .

KB: room(x) --> light(y) & in(y,x)

light(y) & branching-fixtures(y) --> chandelier(y)

Interpreting Compound Nominals

turpentine jar

turpentine(x) jar(y)

fluid(x) & container(y,x)

nn(x,y)

Adjacency to beexplained

Proof is explanationof adjacency

Lexical AmbiguityThe plane taxied to the terminal.

plane(x) & taxi(x,y) & terminal(y)

KB:

airplane(x) --> plane(x)

move-on-ground(x,y) & airplane(x) --> taxi(x,y)

airport-terminal(y) --> terminal(y)

airport(z) --> airplane(x) & airport-terminal(y)

wood-smoother(x) --> plane(x)

ride-in-cab(x,y) & person(x) --> taxi(x,y)

computer-terminal(y) --> terminal(y)

LF:

Lexical Ambiguity

John wanted a loan. He went to the bank.

LF: . . . & loan(l) & . . . . . . & bank(y) & . . .

KB:loan(x) --> financial-institution(y) & issue(y,x)

financial-institution(y) & etc4(y) --> bank1(y)

bank1(y) --> bank(y)

river(z) --> bank2(y) & borders(y,z)

bank2(y) --> bank(y)

Metonymy as Part of Syntax

Syn("read Shakespeare", e,x,-)

Syn("read", e, x, y1)

Syn("Shakespeare", y1, ...)

rel'(y2,y1)Syn("read", e, x, y2)

read'(e,x,y2) text(y2)

play(y2) & write'(e3,y1,y2) & Shakespeare(y1)

Metonymy

SelectionalConstraint

Coercion

RightArgument

Coerce "Shakespeare" into "plays of Shakespeare"

Metonymy as Part of Syntax

Syn("read Shakespeare", e,x,-)

Syn("read", e, x, y1)

Syn("Shakespeare", y1, ...)

rel'(y2,y1)Syn("read", e, x, y2)

read'(e,x,y2) text(y2)

play(y2) & write'(e3,y1,y2) & Shakespeare(y1)

Coercion

Coerce "Shakespeare" into "plays of Shakespeare"

Find a textas Object

Find an authoras Object

Metonymy after Syntax

rel’(e2 y2,y1)

read'(e,x,y2) text’(e1 y2)

play’(e4,y2) & write'(e3,y1,y2) & Shakespeare’(e3 y1)

SelectionalConstraint

Coercion

RightArgument

Coerce "Shakespeare" into "plays of Shakespeare"

read'(e,x,y2) & text’(e1,y2) & rel’(e2,y2,y1) & Shakespeare’(e3,y1)

Pragmatic Loosening as Coercion of Eventualities

Syn("flew to USC", e,x,-)

Syn("flew", e, x, y)

Syn("to USC", y, ...)

rel(e1,e)Syn("flew", e1, x, y)

past(e)

fly'(e1,x,y) --> move-fast'(e,x,y) & imply(e1,e)

Coercion

"Figurative" predicate coerced into inferentiallyrelated predicate.

USC(y)

Pragmatic Loosening as Coercion of Eventualities

rel(e1,e)

past(e)

fly'(e1,x,y) --> move-fast'(e,x,y) & imply(e1,e)

Coercion

"Figurative" predicate coerced into inferentiallyrelated predicate.

USC(y)

past(e) & fly'(e1,x,y) & rel(e1,e) & to’(e2,e1,y) &USC(y)

Pronoun Resolution

The plain was reduced by erosion to its present level.

LF: reduce'(e1,p,l) & plain(p) & erode'(e2,x) & present(e3) & level'(e3,l,y)

KB: To decrease on a vertical scale is to reduce: decrease(p,l,s) & vertical(s) & etc1(p,l,s) --> reduce'(e,p,l)

A flat landform is a plain: landform(p) & flat(p) & etc2(p) --> plain(p)

If a flat thing Y is at a point L on a vertical scale, then L is the level of Y: at'(e,y,l) & on(l,s) & vertical(s) & flat(y) & etc3(e,y,l,s) ---> level'(e,l,y)

One way for a landform to decrease on the altitude scale is to erode: decrease'(x,l,s) & landform(x) & altitude(s) & etc4(x,l,s) ---> erode'(e,x)

One kind of vertical scale is the altitude scale: vertical(s) & etc5(s) --> altitude(s)

Pronoun Resolution

The plain was reduced by erosion to its present level.

KB: decrease(p,l,s) & vertical(s) & etc1(p,l,s) --> reduce'(e,p,l)

landform(p) & flat(p) & etc2(p) --> plain(p)

at'(e,y,l) & on(l,s) & vertical(s) & flat(y) & etc3(e,y,l,s) ---> level'(e,l,y)

decrease'(x,l,s) & landform(x) & altitude(s) & etc4(x,l,s) ---> erode'(e,x)

vertical(s) & etc5(s) --> altitude(s)

Therefore, y (it ) = x = p (the plain )

LF:

reduce’(e1,p,l) &

plain(p) &

erode’(e2,x) &

present(e3) &

level’(e3,l,y)

x=p

x=p

y=p

Schema Recognition and Matching

A bomb exploded at . . . The FMLN claimed responsibility for . . .

Schema Axiom:

bomb-situation(e1,b, . . . , g, e2, . . . ) --->

bomb(b) & explode'(e1,b) & . . .

& terrorist-group(g)

& responsible'(e2,g,e1) & . . .

Recognizing schema yields minimal interpretation.

Outline

Abduction

Solutions to Local Pragmatics Problems using Abduction

How Weighted Abduction Works

Some Systems Using Abduction

Factors in Most Economical Proof

Shortest proof

Fewest and most plausible assumptions

Most salient axioms

Greatest redundancy

Language has a huge amountof implicit redundancy.

Recognizing redundanciesyields more propositions proved

for fewer assumptions

Weighted Abduction

(Stickel, 1988)

1. Goal expressions are assumable at cost (depending on utility of explaining them).

turpentine(x)$3 & nn(x,y)$20 & jar(y)$10

2. Assumability costs can be passed back.

P1w1 & P2

w2 ---> Q

If Q costs $c, then Pi costs wi * c.

Informativity vs. Reliability Trade-off

3. Factoring: Goal expressions can be unified, with minimum cost.

p(x1) & p(x2) ==> p(x)

Helps minimize size of proofs

Weighted Abduction

P1w1 & P2

w2 ---> Q

If w1 + w2 < 1, more specific interpretations are favored. If w1 + w2 > 1, less specific interpretations are favored.

But in

P1.6 & P2

.6 ---> Q

if P1 is proved, it is cheaper to assume P2 than Q. P1 provides evidence for Q.

Weighted Abduction

Factoring can also override less specific abduction:

Axioms: P1.6 & P2

.6 ---> Q1, P2.6 & P3

.6 ---> Q2

Goals: Q1$10 & Q2

$10

Proof: Q1 Q2

P1 & P2 P2 & P3

P1 & P2 & P3

Cost of assuming Q1 & Q2 = $20 Cost of assuming P1 & P2 & P3 = $18

Range of Interpretations

I went to Dallas

I flew to Dallas

I flew to Dallas on Southwest

most reliable

most informative

optimum

Reliability

Informativity

The Form of Axioms Implicative relation between p and q:

(A x,y) p(x,y) --> (E z) q(x,z)

Add eventualities:

(A x,y,e1) p’(e1,x,y) --> (E z,e2) q’(e2,x,z)

Make rule part of explicit knowledge:

(A x,y,e1) p’(e1,x,y) --> (E z,e2) q’(e2,x,z) & imply(e1,e2)

Make the rule defeasible:

(A x,y,e1) p’(e1,x,y)u & etc1(e1,x,y)v --> (E z,e2) q’(e2,x,z) & imply(e1,e2)

Make the rule defeasibly biconditional:

(A x,y,e1) p’(e1,x,y)u1 & etc1(e1,x,y)v1 --> (E z,e2) q’(e2,x,z) & imply(e1,e2)(A x,z,e2) q’(e2,x,z)u2 & etc2(e2,x,y)v2 --> (E y,e1) p’(e1,x,y) & imprel(e2,e1)

The general form for expressing associations between concepts.

What the Numbers Mean:Probability of Occurrence in

InterpretationSpace of events: Occurrences of propositions in best proofs (= correct interpretations) for all texts in corpus.

P1w1 & P2

w2 ---> Q: wi should vary with Pr(Q | Pi).

P1w1 ---> Q

P2w2 ---> Q wi should vary inversely with Pr (Pi | Q),

. with Pr (¬ [P1 & . . . & Pk] | Q) . anchored at 1. .Pk

wk ---> Q

Cost on goal expressions: Utility of finding more specific interpretation.

What the Numbers Mean:Finding Proofs

0: P0 --> Q: Literal freely assumable. e.g., P & S0 --> Q: S is side-effect.

1: P1 --> Q: No added cost to using axiom.

, d << 1, n = number of literals in antecedent: P1

.6 & P2.6 --> Q:

Small added cost for using axiom, favors not backchaining unless partial proof or redundancy.

P --> Q: Must prove.

1+d n

Outline

Abduction

Solutions to Local Pragmatics Problems using Abduction

How Weighted Abduction Works

Some Systems Using Abduction

AQUAINT-I: Question-Answeringfrom Multiple Sources

Show me the region 100 km north of the capital of Afghanistan.

What is the capitalof Afghanistan?

What is the lat/long100 km north?

What is the lat/longof Kabul?

CIAFact Book Geographical

Formula

QuestionDecomposition

via Logical Rules

AlexandrianDigital Library

Gazetteer

Show thatlat/long

Terravision

ResourcesAttached toReasoning

Process

A Complex QueryWhat recent purchases of suspicious equipment has XYZ Corp or its subsidiaries or parent firm made in foreign countries?

subsidiary(x,y)

parent(y,x)

Subsidiaries:XYZ: ABC, ...DEF: ..., XYZ, ...

illegal

biowarfare

DB of bio-equip

Ask User not USA

Purchase: Agent: XYZ, ABC, DEF, ... Patient: anthrax, ... Date: since Jun05 Location: --

Prove Question from Answer

Q: “How did Adolf Hitler die?”QLF: manner(e4) & Adolf(x10) & Hitler(x11) & nn(x12,x10,11) & die’(e4,x12)

ALF: it(x14) & be’(e1,x14,x2) & Zhukov(x1) & ’s(x2,x1) & soldier(x2) & plant’(e2,x2,x3) & Soviet(x3) & flag(x3) & atop(e2,x4) & Reichstag(x4) & on(e2,x8) & May(x5) & 1(x6) & 1945(x7) & nn(x8,x5,x6,x7) & day(x9) & Adolf(x10) & Hitler(x11) & nn(x12,x10,x11) & commit’(e3,x12,e5) & suicide’(e5,x12)A: “It was Zhukov’s soldiers who planted a Soviet flag atop the Reichstag on May 1, 1945, a day after Adolf Hitler committed suicide.”

“suicide” is troponym of “kill”: suicide’(e5,x12) --> kill’(e5,x12,x12) & manner(e5)

Gloss of “kill”: kill’(e5,x12,x12) <--> cause’(e5,x12,e4) & die’(e4,x12)

Gloss of “suicide”: suicide’(e5,x12) <--> kill’(e5,x12,x12)

e4=e5?

The Search Space Problem

120,000 glosses --> 120,000 axiomsTheorem proving would take forever.

Lexical chains / marker passing: Try to find paths between Answer Logical Form and Question Logical Form. Ignore the arguments; look for links between predicates in XWN; it becomes a graph traversal problem (e.g., confuse “buy”, “sell”) Observation: All proofs use chains of inference no longer than 4 steps Carry out this marker passing only 4 levels out

Q: “What Spanish explorer discovered the Mississippi River?”Candidate A: “Spanish explorer Hernando de Soto reached the Mississippi River in 1536.”Lexical chain: discover-v#7 --GLOSS--> reach-v#1

Set of support strategy: Use only axioms that are on one of these paths. 120,000 axioms ==> several hundred axioms

Relaxation (Assumptions)

Rarely or never can the entire Question Logical Form be proved from the Answer Logical Form ==> We have to relax the Question Logical Form

“Do tall men succeed?”

Logical Form: tall’(e1,x1) & x1=x2 & man’(e2,x2) & x2=x3 & succeed’(e3,x3)

Remove these conjuncts from what has to be proved, one by one, in some order, and try to prove again.

E.g., we might find a mention of something tall and a statement that men succeed.One limiting case: We find a mention of success.

Penalize proof for every relaxation, and pick the best proof.

Abduction

Observable: QGeneral principle: P --> Q

Conclusion, assumption, or explanation: P

Inference to thebest explanation

In the LCC QA system: The question is the observable: Hitler died The XWN glosses and troponyms are suicide --> kill --> die the general principles: The answer is the explanation: Hitler committed suicide

Relaxation is the assumptions you have to make to get the proof to go through.

Abduction: Try to prove Q the best you can; Make assumptions where you have to.