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Packed Computation of Exact Meaning Representations Iddo Lev Department of Computer Science Stanford University Outline Motivation From Syntax to Semantics Packed Computation Conclusion April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 2 Natural Language Understanding • How can we improve accuracy? • Let’s take it for a moment to the extreme – Exact NLU applications April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 3 Example: Logic Puzzles Six sculptures—C, D, E, F, G, and H—are to be exhibited in rooms 1, 2, and 3 of an art gallery. Sculptures C and E may not be exhibited in the same room. Sculptures D and G must be exhibited in the same room. If sculptures E and F are exhibited in the same room, no other sculpture may be exhibited in that room. At least one sculpture must be exhibited in each room, and no more than three sculptures may be exhibited in any room. 1. If sculpture D is exhibited in room 3 and sculptures E and F are exhibited in room 1, which of the following may be true? (A) Sculpture C is exhibited in room 1. (B) No more than 2 sculptures are exhibited in room 3. (C) Sculptures F and H are exhibited in the same room. (D) Three sculptures are exhibited in room 2. (E) Sculpture G is exhibited in room 2. April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 4 Example: Logic Puzzles If sculptures E and F are exhibited in the same room, no other sculpture may be exhibited in that room. exact meaning representation: x.[(room(x) exhibited-in(E,x) exhibited-in(F,x)) ¬y.sculpture(y) y E y F exhibited-in(y,x)] April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 5 Example: • MSCS Degree Requirements – A candidate is required to complete a program of 45 units. At least 36 of these must be graded units, passed with an average 3.0 (B) grade point average (GPA) or higher. The 45 units may include no more than 21 units of courses from those listed below in Requirements 1 and 2. … – Has Patrick Davis completed the program? – Can/must Patrick Davis take CS287? • Similar to logic puzzles: – General constraints + specific situation April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 6 Exact NLU • More examples – Word problems • Logic puzzles • Math, physics, chemistry questions – Simple regulation texts, controlled language – NL interfaces to databases • Like SQL, but looks like NL • In these tasks – “Almost correct” (“only slightly wrong”) is not good enough – Simple approximations won’t do • E.g. syntactic matching between text and questions • Because answer does not appear explicitly in the text – Need exact calculation of NL meaning representations • Answer needs to be inferred from the text • Need to carefully combine information/meaning throughout the text April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 7 Structural Semantics • Need to rely on high-quality meaning representations and linguistic knowledge – In particular, structural semantics • Meaning of functional words • Logical structure of sentences • Essential for exact NLU tasks • Could also improve precision of other NLP tasks • T: Michael Melvill guided a tiny rocket-ship more than 100 kilometers above the Earth. • H: A rocket-ship was guided more than 80 kilometers above the Earth. Follows • H: A rocket-ship was guided more than 120 kilometers above the Earth. Does not follow • Relatively small size of knowledge • Functional: #functional words 400 #grammar rules 400 • Lexical: #verb frames 45,000 #nouns > 100,000 April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 8 My Dissertation • How to map syntactic analysis to meaning representations • How to compute all meaning representations efficiently Focus of this talk • Linguistic analysis of advanced NL constructions using the above framework – anaphora (interaction with truth conditions) – comparatives – reciprocals (each other, one another) – same/different • How to translate meaning representations to inference representations (FOL) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 9 Structural Semantics Challenges • When analyzing one sentence: – (1) Bills 2 and 6 are paid on the same day as each other. • it might seem enough to use: – x.day(x)paid-on(bill2,x)paid-on(bill6,x) • But this is not enough when we consider other sentences: – (2) John, Mary, and Frank like each other. – each_other({john,mary,frank}, xy.like(x,y)) • Goal – Uniformity: one analysis of “each other” for both (1) and (2). • Should interact correctly with “the same” in (1). – Solution should also be consistent with “different”, “similar”: • Men and women have a different sense of humor (than each other). April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 10 Outline Motivation From Syntax to Semantics Packed Computation Conclusion April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 11 From Syntax to Semantics • How do we get from one parse tree to a semantic representation? – Classic Method (Montague): one-to-one correspondence: assign a lambda-term to each syntactic node S x. [dog(x) bark(x)] λR. x. [dog(x) R(x)] NP VP | Det Noun V every dog barks λP.λR. x. [P(x) R(x)] λy.dog(y) λz. bark(z) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 12 Problem 1: Floating Operators S NP VP V NP PP NP Frank introduced Rachel to Patrick. introduce-to(frank, rachel, patrick) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 13 Problem 1: Floating Operators S NP VP V NP PP NP N’ RC Det VP N VP NP Frank introduced Rachel to every person who visited me that summer. every(λx.person(x)visit(x,me), λx.introduce-to(frank, rachel, x)) every(P,Q) x. [P(x) Q(x)] April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 14 Problem 1: Floating Operators S S NP VP NP VP N’ N’ Adj N Adj N A brave sailor walked by. An occasional sailor walked by. a(λx.[sailor(x)brave(x)], occasionally(a(λx.sailor(x), λx.walk-by(x)) λx.walk-by(x))) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 15 Problem 2: More Than One Meaning “In this country, a woman gives birth every 15 minutes. Our job is to find that woman, and stop her.” -- Groucho Marx every 15 minutes a woman a woman every 15 minutes gives birth gives birth You may not smoke. All these books are not interesting. You may not succeed. All that glitters is not gold. April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 16 Glue Semantics • Glue Semantics: A flexible framework for mapping syntax to semantics – Pieces of syntax correspond to pieces of semantics – Pieces of semantics combine with each other according to constraints • Like jigsaw puzzle, but possibly with more than one solution – Not a simple one-to-one mapping • References – Dalrymple et al. Semantics and Syntax in Lexical Functional Grammar. 1999 Mary Dalrymple. Lexical Functional Grammar. 2001 Asudeh, Crouch, Dalrymple. The syntax-semantics interface. 2002 April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 17 Glue Semantics (simplified example) S NP VP NP Name V Name statements John saw Mary mary xy.see(x,y) john April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 18 Glue Semantics (simplified example) Sa b NP VP NP c Name V Name statements John saw Mary mary : c xy.see(x,y) : b c a john : b derivation prover john : b xy.saw(x,y) : b c a mary : c y.saw(john,y) : c a saw(john,mary) : a gain: order of combination does not have to follow tree hierarchy April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 19 Problem 1: Floating Operators S S NP VP NP VP λx.[sailor(x)brave(x)] λQλR.occasionally[Q(λx.sailor(x),R)] N’ N’ Adj N Adj N A brave sailor walked by. An occas. sailor walked by. λPλR.a(P,R) λx.sailor(x) λx.walk-by(x) λPλR.a(P,R) λx.sailor(x) λx.walk-by(x) λPλx.[P(x)brave(x)] λPλQλR.occasionally[Q(P,R)] a(λx.[sailor(x)brave(x)], occasionally[a(λx.sailor(x), λx.walk-by(x)) λx.walk-by(x))] April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 20 Glue Semantics S a Flexible handling of b NP VP floating operators. N’ c λPλR.a(P,R) : c (b a) a Adj N An occas. sailor walked by. λx.sailor(x) : c λx.walk-by(x) : b a c c (b a) a λS.occasionally[S] : a a ba (b a) a a aa a occasionally[a(λx.sailor(x), λx.walk-by(x))] April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 21 Glue Semantics (simplified example) Can yield more than one meaning. A woman gives birth every 15 minutes. “gives birth” G:a “a woman” A: a a “every 15 minutes” E:aa two possible derivations: G:a A: a a G:a E:aa A(G) : a E:aa E(S) : a A:aa E(A(G)) : a A(E(S)) : a April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 22 Glue Semantics • Shared labels constrain how statements combine – “Resource Sensitive”: Use each statement exactly once – Inference rules: Application Abstraction [x:A] :A :AB ¦ ():B :B Linear Logic x.:AB (implicative fragment) • In Glue Semantics, can impose further constraints on combinations. April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 23 Outline Motivation From Syntax to Semantics Packed Computation Conclusion April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 24 Ambiguity • Flying planes can be dangerous. Therefore, only licensed pilots are allowed to do it. • Flying planes can be dangerous. Therefore, some people are afraid to ride in them. • We cannot always disambiguate the sentence just by looking at the sentence itself. • We sometimes need to take the larger context and information into account. April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 25 Ambiguity Alternatives multiply across layers… Morphology Reasoning Semantics Syntax KR Text … so we can’t keep all the alternatives separately April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 26 Early Pruning • Select most likely analysis at each level • Oops: Strong constraints may reject the so-far-best (and only) option Statistics X X X Morphology Reasoning Semantics Syntax X KR Text Locally less likely option but globally correct April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 27 Packing The sheep liked the fish. More than one sheep? More than one fish? Options multiplied out The sheep-sg liked the fish-sg. The sheep-pl liked the fish-sg. The sheep-sg liked the fish-pl. The sheep-pl liked the fish-pl. Options packed sg sg The sheep liked the fish pl pl Packed representation: – Encodes all analyses without loss of information – Common items represented and computed just once April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 28 Packing • Calculate compactly all analyses at each stage • Push ambiguities through the stages • Possibly, filter and keep only N-best at each stage in a packed form (not only 1-best) • This approach is being pursued in the XLE system at PARC (and Powerset Inc.) – (Maxwell & Kaplan ’89,93,95) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 29 Packing In Syntax: Chart Parser A chart parser for a context-free grammar can compute an exponential number of parse trees in O(n3) time by representing and computing them compactly. Instead of separately: we have: April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 30 Packed Structures XLE manages natural language ambiguity by packing similar structures and managing them under a free-choice space C-structure forest Packed F-structure Choice Space: true A1 A2 A1 A2 false April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 31 Currently in XLE Text semantic rewrite rules FST morph. glue glue spec. prover parser unpack F-str1 Glue1 MR1 pack C-str F-str : : MR KR : : C-F F-strn Gluen MRn answer = packed = packed calculation + possibly filter N-best April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 32 The Goal Text FST morph. parser Glue C-str F-str MR KR statements glue glue C-F prover spec. answer = packed = packed calculation + possibly filter N-best April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 33 Goal: Packed Meaning Representation Bill saw the girl with the telescope. a:1 e. see(e) agent(e,bill) a:2 e. see(e) agent(e,bill) theme(e,the(x.girl(x)) theme(e, the(x. girl(x) with(e,the(y.tele(y))) with(x,the(y.tele(y))) ) e. see(e) agent(e,bill) ● ●● theme(e, the(x. ● )) ●● girl(x) with(●,the(y.tele(y))) x e packed meaning representation April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 34 Glue Specification Glue specification – connecting syntactic and semantic pieces NTYPE(f, NAME), PRED(f, p) p : f NTYPE(f, COMMON), PRED(f, p) λx.p(x) : fv fr F-Structure glue statements john : a λx.cake(x) : bv br “John ate the cake.” April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 35 Packed Glue Input Packed F-structure NTYPE(f, NAME), PRED(f, p) p : f e Glue specification {1} e.see(e) : aveart {2} P.e.P(e) : (aveart)at {3} bill : be “Bill saw the girl with the telescope.” {4} xPe.P(e)agent(e,x) : be(aveart)(aveart) {5} P.the(P) : (gvegrt)ge {6} x.girl(x) : gvegrt This combines {7} xPe.P(e)theme(e,x) : ge(aveart)(aveart) Glue Semantics {8} P.the(P) : (hvehrt)he + packing {9} x.tele(x) : hvehrt {10} A1: yPe.P(e)with(e,y) : he(aveart)(aveart) at the input level {11} A2: yPx.P(x)with(x,y) : he(gvegrt)(gvegrt) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 36 Non-packed Prover (Hepple’96) Rule: Input: : A | S1 : AB | S2 f : c c d q:c r:c () : B | S1 S2 provided S1 S2 = Chart: meaning category span f c c d {1} q c {2} cannot combine: r c {3} {2}{1,2} f(q) cd {1,2} f(r) cd {1,3} complete derivation f(q,r) d {1,2,3} Output: (all indices were used) f(r,q) d {1,2,3} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 37 Syntactic Ambiguity “Time flies like an arrow. Fruit-flies like a banana.” -- Groucho Marx April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 38 Naive Packed Algorithm • – A1: [[John]a thinks that [[time]d flies [like [an arrow]c]]b]g – A2: [[John]a thinks that [[time flies]f like [an arrow]c]b]g • The chart algorithm will discover one history for [[time]d flies [like [an arrow]c]]b under A1 • It may then continue under A1 with “John thinks that” • It will later discover a history for [[time flies]f like [an arrow]c]b under A2 • So it will have to redo the work for “John thinks that” under A2 April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 39 Non-Packed Prover – Forget about meaning terms for now • (can reconstruct them after the derivation finishes) – Combine histories according to topological order of category graph {1} {2} {3} {4} ab a ac category graph mean. category span {5} q ab {1} bcd b {1,2} c {2,4} {1,3} {3,4} p a {2} {1,2,5} r a {3} cd {1,3,5} s ac {4} t bcd {5} u df {6} t(q(p),s(r)) d t(q(r),s(p)) df {1,2,3,4,5} {6} f {1,2,3,4,5,6} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 40 Packed Derivation • (Simplified example) – A1: [[John]a thinks that [[time]d flies [like [an arrow]c]]b]g – A2: [[John]a thinks that [[time flies]f like [an arrow]c]b]g premises choice john a {1} 1 think abg {2} anarrow c {3} time d {4} A1 fly deb {5} like ce {6} timeflies f {7} A2 like fcb {8} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 41 Packed Derivation • (Simplified example) – A1: [[John]a thinks that [[time]d flies [like [an arrow]c]]b]g – A2: [[John]a thinks that [[time flies]f like [an arrow]c]b]g premises choice john a {jn} 1 think abg {th} anarrow c {ar} time d {t} A1 fly deb {f} like ce {k1} timeflies f {tf} A2 like fcb {k2} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 42 Packed Derivation Imagine how each derivation works separately; then figure out how to pack. premises choice john a {jn} 1 {f} {t} {k1} {ar} think abg {th} anarrow c {ar} time d {t} A1 {k1,ar} {jn} {th} fly deb {f} {t,f} like ce {k1} {t,f,k1,ar} {jn,th} timeflies f {tf} A2 like fcb {lk2} {jn,th,t,f,k1,ar} Category graph April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 43 Packed Derivation Imagine how each derivation works separately; then figure out how to pack. {tf} {k2} premises choice john a {jn} 1 {ar} think abg {th} {tf,k2} anarrow c {ar} {tf,k2,ar} time d {t} A1 {jn} {th} fly deb {f} like ce {lk1} {jn,th} timeflies f {tf} A2 like fcb {k2} {jn,th,tf,k2,ar} Category graph April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 44 Packed Derivation Imagine how each derivation works separately; then figure out how to pack. {tf} {k2} premises choice john a {j} 1 {f} {t} {k1} {ar} think abg {th} {tf,k2} anarrow c {a} time d {t} A1 {k1,ar} {jn} {th} fly deb {f} {t,f} A2:{tf,k2,ar} like ce {k1} A1:{t, f,k1,ar} {jn,th} timeflies f {tf} A2 1:{ar} A1:{t, f,k1} A2:{tf,k2} like fcb {k2} {jn,th,t,f,k1,ar} {jn,th,tf,k2,ar} 1:{jn,th,ar} A1:{t, f,k1} A2:{tf,k2} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 45 Packed Derivation only possible in A1 history under A1 under A2 packed span h1 {ar} {ar} 1:{ar} h2 {k1,ar} A1:{k1,ar} h3 {t,f} A1:{t,f} h4 {t,f,k1,ar} A1:{t,f,k1,ar} h5 {tf,k2} A2:{tf,k2} h6 {tf,k2,ar} A2:{tf,k2,ar} h7 {t,f,k1,ar} {tf,k2,ar} 1:{ar} A1:{t,f,k1} A2:{tf,k2} h8 {jn,th} {jn,th} 1:{jn,th} h9 {jn,th,t,f,k1,ar} {jn,thtf,k2,ar} 1:{jn,th,ar} A1:{t,f,k1} A2:{tf,k2} {tf} {k2} packed common part {f} {t} {k1} {ar} {tf,k2} {k1,ar} {t,f} A2:{tf,k2,ar} {jn} {th} A1:{t, f,k1,ar} {jn,th} 1:{ar} A1:{t, f,k1} A2:{tf,k2} 1:{jn,th,ar} A1:{t, f,k1} A2:{tf,k2} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 46 Packed Derivation • Two histories with categories A and AB can be combined: – original algorithm: if their spans are disjoint – packed algorithm: can combine them in all contexts in which their spans are disjoint original combination: A | S1 AB | S2 provided S1 S2 = B|S and S = S1 S2 packed combination: provided C1 C2 0 C1 | A | PS1 C2 | AB | PS2 and combinable(PS1, PS2, C) C | B | PS and PS = union(C, PS1, PS2) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 47 Packed Derivation • Two histories with categories A and AB can be combined: – original algorithm: if their spans are disjoint – packed algorithm: can combine them in all contexts in which their spans are disjoint packed combination: provided C1 C2 0 C1 | A | PS1 C2 | AB | PS2 and combinable(PS1, PS2, C) C | B | PS and PS = union(C, PS1, PS2) combinable: 1:{3,4} 1:{5,6,7} 1:{3,4,5,6,7} combinable: 1:{3},A1:{6,7} 1:{4,5},A2:{6,8} 1:{3,4,5,6},A1:{7},A2:{8} combinable: A1:{6},A2:{7} A1:{6},A2:{8} A2:{7,8} non-combinable: 1:{4},A1:{6} 1:{5,6},A2:{4} (6 is in A1 in both, 4 is in A2 in both) A1:{4,6} A2:{4} A1:{5,6} A2:{4,5,6} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 48 Packed Derivation • Two histories with the same category can be packed: – original algorithm: if their spans are identical – packed algorithm: if their spans are identical in the shared contexts can pack: 1:{3,4,5} 1:{3,4,5} 1:{3,4,5} can pack: A1:{1},A2:{2} A2:{2},A3:{3} A1:{1},A2:{2},A3:{3} can pack: A1:{t,f,k1,ar} A2:{tf,k2,ar} 1:{ar}, A1:{t,f,k1}, A2:{tf,k2} cannot pack: 1:{5},A1:{6} 1:{5},A2:{7} ({5,6}{5} in A1 , {5}{5,7} in A2)) A1:{5,6} A2:{5} A1:{5} A2:{5,7} {ar} A2:{tf,k2,ar} A1:{t, f,k1,ar} 1:{ar} A1:{t, f,k1} A2:{tf,k2} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 49 Packed Derivation Reconstruction of packed meaning representation: history packed span meaning h1 1:{ar} l1 : anarrow h2 A1:{k1,ar} like(l1) h3 A1:{t,f} fly(time) h4 A1:{t,f,k1,ar} fly(time,like(l1)) h5 A2:{tf,k2} like(timeflies) h6 A2:{tf,k2,ar} like(timeflies,l1) h7 1:{ar} A1:{t,f,k1} A2:{tf,k2} A1:fly(time,like(l1)) A2:like(timeflies,l1) h8 1:{jn,th} think(john) h9 1:{jn,th,ar} A1:{t,f,k1} A2:{tf,k2} think(john, ●) A1 A2 fly(time,like(●)) like(timeflies,●) anarrow category graph packed meaning representation April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 50 Packed Derivation • What if the category graph has cycles? – Calculate strongly connected components (SCCs) and the induced directed-acyclic graph (DAG) (+ topological sort) – In each SCC, run basic algorithm to find all possibilities – If SCC is simple (X, XX) then optimize: use as much material as possible before moving out of the cycle {2} {3} {4} {1} XX X {1} category graph {1,2} {1,3} {1,4} {1,2,3} {1,2,4} {1,3,4} {1,2,3,4} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 51 Packed Derivation [girl [with the telescope]]A2 A2:{wt} 1:{grl} XX X 1:{grl} A1:{grl} A2:{grl,wt} category graph 1:{grl}, A2:{wt} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 52 Packed Derivation Category graph {1} e.see(e) : aveart {2} P.e.P(e) : (aveart)at 1:{8} 1:{9} {3} bill : be (hvehrt)he hvehrt A2:{11} {4} xPe.P(e)agent(e,x) : be(aveart)(aveart) he(gvegrt)(gvegrt) {5} P.the(P) : (gvegrt)ge he 1:{8,9} {6} x.girl(x) : gvegrt A2:{8,9,11} {7} xPe.P(e)theme(e,x) : ge(aveart)(aveart) (gvegrt)(gvegrt) {8} P.the(P) : (hvehrt)he {9} x.tele(x) : hvehrt {10} A1: yPe.P(e)with(e,y) : he(aveart)(aveart) (gvegrt)ge gvegrt {11} A2: yPx.P(x)with(x,y) : he(gvegrt)(gvegrt) 1:{6},A2:{8,9,11} A1:{10} ge geaetaet 1:{3} heaetaet beaetaet be 1:{5,6,7}, 1:{3,4} A1:{8,9,10} Need to calculate A2:{8,9,11} strongly-connected components before aetaet 1:{2} aetat topological sort. aet 1:{1,3,4,5,6,7,8,9}, A1:{10},A2:{11} at1:{1,2,3,4,5,6,7,8,9}, packing in a cycle A1:{10},A2:{11} April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 53 Outline Motivation From Syntax to Semantics Packed Computation Conclusion April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 54 My Dissertation • How to map syntactic analysis to meaning representations • How to compute all meaning representations efficiently Focus of this talk • Linguistic analysis of advanced NL constructions using the above framework – anaphora (interaction with truth conditions) – comparatives – reciprocals (each other, one another) – same/different • How to translate meaning representations to inference representations (FOL) April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 55 Summary • Mapping syntax to exact meaning representations using Glue Semantics – More powerful than traditional approach – Easier for users, more principled than semantic rewrite rules – Covered advanced NL constructions • Computing all meaning representations efficiently – Input: packed syntactic analysis – Output: packed meaning representation Pushing packed ambiguities through the semantics stage April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 56 Future Work • Researchers can use this work as a basis – Use this in applications • Logic puzzles, word problems, NLIDB, regulation texts – Extend this approach to additional NL constructions • (requires some linguistic research) – Extend idea of packing to anaphora/plurality and back-end inference stages • Some initial work on packed reasoning at PARC – Extend statistical disambiguation to packed semantic structures April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 57 Thanks • Stanley Peters • Dick Crouch • Chris Manning • Mike Genesereth • Johan van Benthem • NLTT group at PARC • Ivan Sag • Bill MacCartney, Mihaela Enachescu, Powerset Inc. • Beth Nowadnick April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 58