CS 544 Lecture 3 4 Interpretation as Abduction

CS 544: Lecture 3. 4 Interpretation 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, e 1, e 2, e 3, e 4, e 5) Rexists(e 5) & again'(e 5, e 3) & not'(e 3, e 2) & past'(e 2, e 4) & work'(e 4, j) & John'(e 1, j) OR again(e 3) & not'(e 3, e 2) & past'(e 2, e 4) & work'(e 4, 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 cause Storm Explain Relations in Environment Explain Entities in Environment

Interpreting the Environment: Picking the Best Explanation boat in tree down chopped down crane storm ?

Interpreting the Environment: Picking the Best Explanation boat in tree down in magazine chopped down crane storm ad agency advertisement

Interpreting the Environment observable-1 observable-2 underlying cause observable-3 underlying cause deeper underlying cause In Abduction, best explanation can 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 implicational structure 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 2. 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. Speaker MB Hearer Utt Uniform framework for 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) p 1(x) & p 2(x, z) --> ( y) q 1(y, x) & q 2(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'(e 1, x, y) --> move-fast'(e, x, y) & imply(e 1, e) (Flying implies moving fast)

Nonmonotonicity or Defeasibility bird(x)w 1 & etc 1(x)w 2 --> fly(x) You can never prove this, but you can assume it for a cost. This may yield lowest cost interpretation. mammal(x)w 3 & etc 2(x)w 4 <--> 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. New Information 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) Definite Reference Metonymy work-for(x, y) --> rel(x, y) in(O, B), Boston(B) in(y, z) --> nn(z, y) Compound Nominal “Local Pragmatics” problems solved as a by-product Syntax : Parse Tree : : Interpretation : Proof Graph

Definite Reference John bought a new car. LF: . . . & car(c) &. . . The engine is already broken. . & 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) nn(x, y) Adjacency to be explained jar(y) fluid(x) & container(y, x) Proof is explanation of adjacency

Lexical Ambiguity The plane taxied to the terminal. LF: 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)

Lexical Ambiguity John wanted a loan. LF: . . . & loan(l) &. . . He went to the bank. . & bank(y) &. . . KB: loan(x) --> financial-institution(y) & issue(y, x) financial-institution(y) & etc 4(y) --> bank 1(y) --> bank(y) river(z) --> bank 2(y) & borders(y, z) bank 2(y) --> bank(y)

Metonymy as Part of Syntax Syn("read Shakespeare", e, x, -) Syn("Shakespeare", y 1, . . . ) Syn("read", e, x, y 1) Metonymy Syn("read", e, x, y 2) rel'(y 2, y 1) Selectional Constraint read'(e, x, y 2) Right Argument text(y 2) Coercion play(y 2) & write'(e 3, y 1, y 2) & Shakespeare(y 1) Coerce "Shakespeare" into "plays of Shakespeare"

Metonymy as Part of Syntax Syn("read Shakespeare", e, x, -) Find an author as Object Find a text as Object Syn("Shakespeare", y 1, . . . ) Syn("read", e, x, y 1) Syn("read", e, x, y 2) read'(e, x, y 2) text(y 2) rel'(y 2, y 1) Coercion play(y 2) & write'(e 3, y 1, y 2) & Shakespeare(y 1) Coerce "Shakespeare" into "plays of Shakespeare"

Metonymy after Syntax read'(e, x, y 2) & text’(e 1, y 2) & rel’(e 2, y 1) & Shakespeare’(e 3, y 1) rel’(e 2 y 2, y 1) Selectional Constraint read'(e, x, y 2) Right Argument text’(e 1 y 2) Coercion play’(e 4, y 2) & write'(e 3, y 1, y 2) & Shakespeare’(e 3 y 1) Coerce "Shakespeare" into "plays of Shakespeare"

Pragmatic Loosening as Coercion of Eventualities Syn("flew to USC", e, x, -) Syn("to USC", y, . . . ) Syn("flew", e, x, y) Syn("flew", e 1, x, y) past(e) rel(e 1, e) USC(y) Coercion fly'(e 1, x, y) --> move-fast'(e, x, y) & imply(e 1, e) "Figurative" predicate coerced into inferentially related predicate.

Pragmatic Loosening as Coercion of Eventualities past(e) & fly'(e 1, x, y) & rel(e 1, e) & to’(e 2, e 1, y) &USC(y) rel(e 1, e) past(e) USC(y) Coercion fly'(e 1, x, y) --> move-fast'(e, x, y) & imply(e 1, e) "Figurative" predicate coerced into inferentially related predicate.

Pronoun Resolution The plain was reduced by erosion to its present level. LF: reduce'(e 1, p, l) & plain(p) & erode'(e 2, x) & present(e 3) & level'(e 3, l, y) KB: To decrease on a vertical scale is to reduce: decrease(p, l, s) & vertical(s) & etc 1(p, l, s) --> reduce'(e, p, l) A flat landform is a plain: landform(p) & flat(p) & etc 2(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) & etc 3(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) & etc 4(x, l, s) ---> erode'(e, x) One kind of vertical scale is the altitude scale: vertical(s) & etc 5(s) --> altitude(s)

Pronoun Resolution The plain was reduced by erosion to its present level. y=p KB: decrease(p, l, s) & vertical(s) & etc 1(p, l, s) --> reduce'(e, p, l) LF: reduce’(e 1, p, l) & x=p landform(p) & flat(p) & etc 2(p) --> plain(p) & x=p at'(e, y, l) & on(l, s) & vertical(s) & flat(y) & etc 3(e, y, l, s) ---> level'(e, l, y) erode’(e 2, x) & decrease'(x, l, s) & landform(x) & altitude(s) & etc 4(x, l, s) ---> erode'(e, x) vertical(s) & etc 5(s) --> altitude(s) Therefore, y (it ) = x = p (the plain ) present(e 3) & level’(e 3, l, y)

Schema Recognition and Matching A bomb exploded at. . . The FMLN claimed responsibility for. . . Schema Axiom: bomb-situation(e 1, b, . . . , g, e 2, . . . ) ---> bomb(b) & explode'(e 1, b) &. . . & terrorist-group(g) & responsible'(e 2, g, e 1) &. . . 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 amount of implicit redundancy. Recognizing redundancies yields 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. P 1 w 1 & P 2 w 2 ---> 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(x 1) & p(x 2) ==> p(x) Helps minimize size of proofs

Weighted Abduction P 1 w 1 & P 2 w 2 ---> Q If w 1 + w 2 < 1, more specific interpretations are favored. If w 1 + w 2 > 1, less specific interpretations are favored. But in P 1. 6 & P 2. 6 ---> Q if P 1 is proved, it is cheaper to assume P 2 than Q. P 1 provides evidence for Q.

Weighted Abduction Factoring can also override less specific abduction: Axioms: P 1. 6 & P 2. 6 ---> Q 1, P 2. 6 & P 3. 6 ---> Q 2 Goals: Q 1$10 & Q 2$10 Proof: Q 1 Q 2 P 1 & P 2 & P 3 Cost of assuming Q 1 & Q 2 = $20 Cost of assuming P 1 & P 2 & P 3 = $18

Range of Interpretations I went to Dallas most reliable optimum I flew to Dallas Reliability I flew to Dallas on Southwest most informative 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, e 1) p’(e 1, x, y) --> (E z, e 2) q’(e 2, x, z) Make rule part of explicit knowledge: (A x, y, e 1) p’(e 1, x, y) --> (E z, e 2) q’(e 2, x, z) & imply(e 1, e 2) Make the rule defeasible: (A x, y, e 1) p’(e 1, x, y)u & etc 1(e 1, x, y)v --> (E z, e 2) q’(e 2, x, z) & imply(e 1, e 2) Make the rule defeasibly biconditional: (A x, y, e 1) p’(e 1, x, y)u 1 & etc 1(e 1, x, y)v 1 --> (E z, e 2) q’(e 2, x, z) & imply(e 1, e 2) (A x, z, e 2) q’(e 2, x, z)u 2 & etc 2(e 2, x, y)v 2 --> (E y, e 1) p’(e 1, x, y) & imprel(e 2, e 1) The general form for expressing associations between concepts.

What the Numbers Mean: Probability of Occurrence in Interpretation Space of events: Occurrences of propositions in best proofs (= correct interpretations) for all texts in corpus. P 1 w 1 & P 2 w 2 ---> Q: wi should vary with Pr(Q | Pi). P 1 w 1 ---> Q P 2 w 2 ---> Q. . . Pkwk ---> Q wi should vary inversely with Pr (Pi | Q), with Pr (¬ [P 1 &. . . & Pk] | Q) anchored at 1. Cost on goal expressions: Utility of finding more specific interpretation.

What the Numbers Mean: Finding Proofs 0: P 0 --> Q: Literal freely assumable. e. g. , P & S 0 --> Q: S is side-effect. 1: P 1 --> Q: No added cost to using axiom. 1+d n , d << 1, n = number of literals in antecedent: P 1. 6 & P 2. 6 --> Q: Small added cost for using axiom, favors not backchaining unless partial proof or redundancy. P --> Q: Must prove.

Outline Abduction Solutions to Local Pragmatics Problems using Abduction How Weighted Abduction Works Some Systems Using Abduction

AQUAINT-I: Question-Answering from Multiple Sources Show me the region 100 km north of the capital of Afghanistan. Question Decomposition via Logical Rules What is the capital of Afghanistan? What is the lat/long 100 km north? Show that lat/long What is the lat/long of Kabul? Terravision CIA Fact Book Alexandrian Digital Library Gazetteer Geographical Formula Resources Attached to Reasoning Process

A Complex Query What recent purchases of suspicious equipment has XYZ Corp or its subsidiaries or parent firm made in foreign countries? parent(y, x) Ask User illegal not USA subsidiary(x, y) Subsidiaries: XYZ: ABC, . . . DEF: . . . , XYZ, . . . Purchase: Agent: XYZ, ABC, DEF, . . . Patient: anthrax, . . . Date: since Jun 05 Location: -- biowarfare DB of bio-equip

Prove Question from Answer Q: “How did Adolf Hitler die? ” QLF: manner(e 4) & Adolf(x 10) & Hitler(x 11) & nn(x 12, x 10, 11) & die’(e 4, x 12) e 4=e 5? “suicide” is troponym of “kill”: suicide’(e 5, x 12) --> kill’(e 5, x 12) & manner(e 5) Gloss of “kill”: kill’(e 5, x 12) <--> cause’(e 5, x 12, e 4) & die’(e 4, x 12) Gloss of “suicide”: suicide’(e 5, x 12) <--> kill’(e 5, x 12) ALF: it(x 14) & be’(e 1, x 14, x 2) & Zhukov(x 1) & ’s(x 2, x 1) & soldier(x 2) & plant’(e 2, x 3) & Soviet(x 3) & flag(x 3) & atop(e 2, x 4) & Reichstag(x 4) & on(e 2, x 8) & May(x 5) & 1(x 6) & 1945(x 7) & nn(x 8, x 5, x 6, x 7) & day(x 9) & Adolf(x 10) & Hitler(x 11) & nn(x 12, x 10, x 11) & commit’(e 3, x 12, e 5) & suicide’(e 5, x 12) 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. ”

The Search Space Problem 120, 000 glosses --> 120, 000 axioms Theorem 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’(e 1, x 1) & x 1=x 2 & man’(e 2, x 2) & x 2=x 3 & succeed’(e 3, x 3) 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: General principle: Q P --> Q Conclusion, assumption, or explanation: P Inference to the best explanation Abduction: Try to prove Q the best you can; Make assumptions where you have to. 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.