acl acl2011 acl2011-200 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Percy Liang ; Michael Jordan ; Dan Klein
Abstract: Compositional question answering begins by mapping questions to logical forms, but training a semantic parser to perform this mapping typically requires the costly annotation of the target logical forms. In this paper, we learn to map questions to answers via latent logical forms, which are induced automatically from question-answer pairs. In tackling this challenging learning problem, we introduce a new semantic representation which highlights a parallel between dependency syntax and efficient evaluation of logical forms. On two standard semantic parsing benchmarks (GEO and JOBS), our system obtains the highest published accuracies, despite requiring no annotated logical forms.
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract Compositional question answering begins by mapping questions to logical forms, but training a semantic parser to perform this mapping typically requires the costly annotation of the target logical forms. [sent-8, score-0.999]
2 In this paper, we learn to map questions to answers via latent logical forms, which are induced automatically from question-answer pairs. [sent-9, score-0.51]
3 In tackling this challenging learning problem, we introduce a new semantic representation which highlights a parallel between dependency syntax and efficient evaluation of logical forms. [sent-10, score-0.495]
4 On two standard semantic parsing benchmarks (GEO and JOBS), our system obtains the highest published accuracies, despite requiring no annotated logical forms. [sent-11, score-0.49]
5 Answering these types of complex questions compositionally involves first mapping the questions into logical forms (semantic parsing). [sent-13, score-0.648]
6 Supervised semantic parsers (Zelle and Mooney, 1996; Tang and Mooney, 2001 ; Ge and Mooney, 2005; Zettlemoyer and Collins, 2005; Kate and Mooney, 2007; Zettlemoyer and Collins, 2007; Wong and Mooney, 2007; Kwiatkowski et al. [sent-14, score-0.09]
7 , 2010) rely on manual annotation of logical forms, which is expensive. [sent-15, score-0.375]
8 On the other hand, existing unsupervised semantic parsers (Poon and Domingos, 2009) do not handle deeper linguistic phenomena such as quantification, negation, and superlatives. [sent-16, score-0.133]
9 (2010), we obviate the need for annotated logical forms by considering the endto-end problem of mapping questions to answers. [sent-18, score-0.622]
10 However, we still model the logical form (now as a latent variable) to capture the complexities of language. [sent-19, score-0.445]
11 We represent logical forms z as labeled trees, induced automatically from (x, y) pairs. [sent-21, score-0.551]
12 We want to induce latent logical forms z (and parameters θ) given only question-answer pairs (x, y), which is much cheaper to obtain than (x, z) pairs. [sent-22, score-0.509]
13 The core problem that arises in this setting is program induction: finding a logical form z (over an exponentially large space of possibilities) that produces the target answer y. [sent-23, score-0.463]
14 Unlike standard semantic parsing, our end goal is only to generate the correct y, so we are free to choose the representation for z. [sent-24, score-0.053]
15 The dominant paradigm in compositional se- mantics is Montague semantics, which constructs lambda calculus forms in a bottom-up manner. [sent-26, score-0.447]
16 CCG is one instantiation (Steedman, 2000), which is used by many semantic parsers, e. [sent-27, score-0.053]
17 However, the logical forms there can become quite complex, and in the context of program induction, this would lead to an unwieldy search space. [sent-30, score-0.502]
18 (2010), are simpler but lack the full expressive power of lambda calculus. [sent-35, score-0.137]
19 The main technical contribution of this work is a new semantic representation, dependency-based compositional semantics (DCS), which is both simple and expressive (Section 2). [sent-36, score-0.346]
20 The logical forms in this framework are trees, which is desirable for two reasons: (i) they parallel syntactic dependency trees, which facilitates parsing and learning; and (ii) evaluating them to obtain the answer is computationally efficient. [sent-37, score-0.56]
21 Our system outperforms all existing systems despite using no annotated logical forms. [sent-39, score-0.375]
22 1) of dependency-based compositional semantics (DCS), which captures the core idea of using trees to represent formal semantics. [sent-41, score-0.369]
23 2), which handles linguistic phenomena such as quantification, where syntactic and semantic scope diverge. [sent-43, score-0.096]
24 We start with some definitions, using US geography as an example domain. [sent-44, score-0.032]
25 Let V be the set of all values, awnh eixcah minpclelud deosm primitives (e. [sent-45, score-0.035]
26 , 3, CA ∈ V) as well as sets and tuples formed from other v∈alu Ves) (e. [sent-47, score-0.045]
27 , state, count ∈ P), Pw bheich a are just symbols. [sent-52, score-0.031]
28 A world w is mapping from each predicate p ∈ P Ato a rsledt wof tuples; nfogr example, w(state) = {(CA) , (OR) , . [sent-53, score-0.205]
29 h Cereon ceaepchtu predicate irlsd a sre ala rteiloan(possibly infinite). [sent-61, score-0.192]
30 As another ePxample, w(average) = {(S, x¯) : x¯ = |S1|−1 Px∈S1 S(x)}, where a s =et o {f( pairs )S : ¯ixs t=rea |tSed| as Pa xs∈etS-vSal(uxe)d} ,fu wnhcetiroen a S(x) = {y : (x, y) ∈ S} swP aith s edto-vmalauine S1 = {x : (x, y) ∈ S}. [sent-66, score-0.038]
31 T,yh)e logical tfhor dmoms iani nD SCS= are c :a l(lxed,y D) ∈CS S trees, where nodes are labeled with predicates, and edges are labeled with relations. [sent-67, score-0.586]
32 Formally: Definition 1(DCS trees) Let Z be the set of DCS trees, itwiohnere 1 e( DacChS z ∈ Zs) c LoentsZi sts b of (i) a predicate 591 Relations R j0 Σ Xi (join) (aggregate) (execute) E Q C (extract) (quantify) (compare) Table 1: Possible relations appearing on the edges of a DCS tree. [sent-68, score-0.236]
33 r ∈ R (see Teaacbhle 1) aend e a cnhsiilsdt tree e. [sent-84, score-0.103]
34 Figure 2(a) DshCoSws tr an example of a DCS tree. [sent-90, score-0.032]
35 though a DCS tree is a logical form, note that it looks like a syntactic dependency tree with predicates in place of words. [sent-92, score-0.605]
36 It is this transparency between syntax and semantics provided by DCS which leads to a simple and streamlined compositional semantics suitable for program induction. [sent-93, score-0.43]
37 1 Basic Version The basic version of DCS restricts R to join and aggregate ir cel vaetrisoniosn (see TCaSbl ree 1). [sent-95, score-0.268]
38 Ltse tR us st joaritn by considering a DCS tree z with only join relations. [sent-96, score-0.216]
39 Such a z defines a constraint satisfaction problem (CSP) with nodes as variables. [sent-97, score-0.091]
40 The CSP has two types of constraints: (i) x ∈ w(p) for each node x labeled cwoinths predicate p ∈ P; apn)d f (ii) xj = yj0 (the j-th component aotfe x must equal t(hiie) jx 0-th component of y) for each edge (x, y) labeled ∈ R. [sent-98, score-0.407]
41 We say a value v is consistent for a node x if there exists a solution that assigns v to x. [sent-101, score-0.07]
42 The denotation JzKw (z esvoalultuiaotned th oant wass) i gs nths ev s toet xof. [sent-102, score-0.289]
43 Tcohnesi dsetnenotta avtiaolune Jsz oKf the rsoolout tinoonde th (aset ea sFsiiggunsre v v2 t foo xr . [sent-103, score-0.038]
44 withjj0 Computation We can compute the denotation JzKw of a DCS tree z by exploiting dynamic proJgzraKmming on trees (Dechter, 2003). [sent-105, score-0.405]
45 The recurrence iJsz aKs follows: JDp;jj110:c1;··· ;jjm0m:cmEKw (1) \m = w(p) ∩ \{v : Kvji = tj0i,t ∈ JciKw}. [sent-106, score-0.031]
46 i\= \1 At each node, we compute the set of ,ttup ∈le Jsc vK consistent with the predicate at that node (v ∈ w(p)), and Example: major city in California z = hcity; 11 : hmajori ; 11 : hloc; 12 : hCAiii maj1orc1it1yl1o2c C1A λccl∃iomtcy(∃(‘c)‘)∃ ∧ ∧sCm. [sent-107, score-0.193]
47 Aa(js)o∧r(m)∧ c1=(‘ m) ∧1∧( cs1)=∧ ‘1∧ ‘2= s1 (a) DCS tree (b) Lambda calculus formula (c) Denotation: JzKw = {SF, LA, . [sent-108, score-0.133]
48 } Fig(uc)re D2:e n(oa)t aAtino enx:a JmzKple of a DCS tree (written in both the mathematical and graphical notation). [sent-111, score-0.068]
49 Each node is labeled with a predicate, and each edge is labeled with a relation. [sent-112, score-0.212]
50 (b) A DCS tree z with only join relations encodes a constraint satisfaction problem. [sent-113, score-0.307]
51 for each child i, the ji-th component of v must equal the j0i-th component of some t in the child’s denotation (t ∈ JciKw). [sent-115, score-0.321]
52 1 iNonow ( tth ∈e d JucalK importance of trees in DCS is clear: We have seen that trees parallel syntactic dependency structure, which will facilitate parsing. [sent-117, score-0.282]
53 In addition, trees enable efficient computation, thereby establishing a new connection between dependency syntax and efficient semantic evaluation. [sent-118, score-0.244]
54 Aggregate relation DCS trees that only use join relations can represent arbitrarily complex compositional structures, but they cannot capture higherorder phenomena in language. [sent-119, score-0.539]
55 For example, consider the phrase number of major cities, and suppose that number corresponds to the count predicate. [sent-120, score-0.031]
56 It is impossible to represent the semantics of this phrase with just a CSP, so we introduce a new aggregate relation, notated Σ. [sent-121, score-0.198]
57 Consider a tree hΣ : ci, wgrhegosaet ero reotla aitsi ocon,nn noetcatetedd dto Σ a c Choilnds c veira a aΣ t. [sent-122, score-0.134]
58 r eIef hthΣe :dcei-, notation of c is a set of values s, the parent’s denotation is then a singleton set containing s. [sent-123, score-0.249]
59 The deJhnΣot:actiiKon o=f t{hJec Kmiddle node is {s}, example. [sent-126, score-0.07]
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