Transforming Dependency Structures to Logical Forms for Semantic Parsing Siva Reddy†a Oscar Täckström‡ Michael Collins‡b Tom Kwiatkowski‡ Dipanjan Das‡ Mark Steedman† Mirella Lapata† †ILCC, School of Informatics, University of Edinburgh ‡ Google, New York siva.reddy@ed.ac.uk {oscart, mjcollins, tomkwiat, dipanjand}@google.com {steedman, mlap}@inf.ed.ac.uk Abstract The strongly typed syntax of grammar for- malisms such as CCG, TAG, LFG and HPSG offers a synchronous framework for deriving syntactic structures and semantic logical forms. In contrast—partly due to the lack of a strong type system—dependency structures are easy to annotate and have become a widely used form of syntactic analysis for many languages. However, the lack of a type system makes a formal mechanism for deriving logical forms from dependency structures challenging. We address this by introducing a robust system based on the lambda calculus for deriving neo- Davidsonian logical forms from dependency trees. These logical forms are then used for semantic parsing of natural language to Free- base. Experiments on the Free917 and Web- Questions datasets show that our representation is superior to the original dependency trees and that it outperforms a CCG-based representa- tion on this task. Compared to prior work, we obtain the strongest result to date on Free917 and competitive results on WebQuestions. 1 Introduction Semantic parsers map sentences onto logical forms that can be used to query databases (Zettlemoyer and Collins, 2005; Wong and Mooney, 2006), instruct robots (Chen and Mooney, 2011), extract information (Krishnamurthy and Mitchell, 2012), or describe vi- sual scenes (Matuszek et al., 2012). Current systems accomplish this by learning task-specific grammars (Berant et al., 2013), by using strongly-typed CCG grammars (Reddy et al., 2014), or by eschewing the use of a grammar entirely (Yih et al., 2015). aWork carried out during an internship at Google. b On leave from Columbia University. Disney acquired Pixar nnp vbd nnp nsubj dobjroot (a) The dependency tree for Disney acquired Pixar. (nsubj (dobj acquired Pixar) Disney) (b) The s-expression for the dependency tree. λx.∃yz. acquired(xe) ∧ Disney(ya) ∧ Pixar(za) ∧arg1(xe,ya) ∧ arg2(xe,za) (c) The composed lambda-calculus expression. Figure 1: The dependency tree is binarized into its s-expression, which is then composed into the lambda expression representing the sentence logical form. In recent years, there have been significant ad- vances in developing fast and accurate dependency parsers for many languages (McDonald et al., 2005; Nivre et al., 2007; Martins et al., 2013, inter alia). Motivated by the desire to carry these advances over to semantic parsing tasks, we present a robust method for mapping dependency trees to logical forms that represent underlying predicate-argument structures.1 We empirically validate the utility of these logical forms for question answering from databases. Since our approach uses dependency trees as input, we hy- pothesize that it will generalize better to domains that are well covered by dependency parsers than methods that induce semantic grammars from scratch. The system that maps a dependency tree to its log- ical form (henceforth DEPLAMBDA) is illustrated in Figure 1. First, the dependency tree is binarized via an obliqueness hierarchy to give an s-expression that describes the application of functions to pairs 1By “robust”, we refer to the ability to gracefully handle parse errors as well as the untyped nature of dependency syntax. 127 Transactions of the Association for Computational Linguistics, vol. 4, pp. 127–140, 2016. Action Editor: Christopher Potts. Submission batch: 12/2015; Published 4/2016. c©2016 Association for Computational Linguistics. Distributed under a CC-BY 4.0 license. mailto:siva.reddy@ed.ac.uk mailto:oscart@google.com mailto:mjcollins@google.com mailto:tomkwiat@google.com mailto:dipanjand@google.com mailto:steedman@inf.ed.ac.uk mailto:mlap@inf.ed.ac.uk of arguments. Each node in this s-expression is then substituted for a lambda-calculus expression and the relabeled s-expression is beta-reduced to give the log- ical form in Figure 1(c). Since dependency syntax does not have an associated type theory, we introduce a type system that assigns a single type to all con- stituents, thus avoiding the need for type checking (Section 2). DEPLAMBDA uses this system to gener- ate robust logical forms, even when the dependency structure does not mirror predicate-argument relation- ships in constructions such as conjunctions, prepo- sitional phrases, relative clauses, and wh-questions (Section 3). These ungrounded logical forms (Kwiatkowski et al., 2013; Reddy et al., 2014; Krishnamurthy and Mitchell, 2015) are used for question answer- ing against Freebase, by passing them as input to GRAPHPARSER (Reddy et al., 2014), a system that learns to map logical predicates to Freebase, result- ing in grounded Freebase queries (Section 4). We show that our approach achieves state-of-the-art per- formance on the Free917 dataset and competitive performance on the WebQuestions dataset, whereas building the Freebase queries directly from depen- dency trees gives significantly lower performance. Finally, we show that our approach outperforms a di- rectly comparable method that generates ungrounded logical forms using CCG. Details of our experimen- tal setup and results are presented in Section 5 and Section 6, respectively. 2 Logical Forms We use a version of the lambda calculus with three base types: individuals (Ind), events (Event), and truth values (Bool). Roughly speaking individuals are introduced by nouns, events are introduced by verbs, and whole sentences are functions onto truth values. For types A and B, we use A×B to denote the product type, while A → B denotes the type of functions mapping elements of A to elements of B. We will make extensive use of variables of type Ind × Event. For any variable x of type Ind × Event, we use x = (xa,xe) to denote the pair of variables xa (of type Ind) and xe (of type Event). Here, the subscript denotes the projections ·a : Ind× Event → Ind and ·e : Ind×Event → Event. An important constraint on the lambda calculus system is as follows: All natural language con- stituents have a lambda-calculus expression of type Ind×Event → Bool. A “constituent” in this definition is either a sin- gle word, or an s-expression. S-expressions are defined formally in the next section; examples are (dobj acquired Pixar) and (nsubj (dobj acquired Pixar) Disney). Essen- tially, s-expressions are binarized dependency trees, which include an ordering over the different dependencies to a head (in the above the dobj modifier is combined before the nsubj modifier). Some examples of lambda-calculus expressions for single words (lexical entries) are as follows: acquired ⇒ λx. acquired(xe) Disney ⇒ λy. Disney(ya) Pixar ⇒ λz. Pixar(za) An example for a full sentence is as follows: Disney acquired Pixar ⇒ λx.∃yz. acquired(xe) ∧ Disney(ya) ∧Pixar(za) ∧ arg1(xe,ya) ∧ arg2(xe,za) This is a neo-Davidsonian style of analysis. Verbs such as acquired make use of event variables such as xe, whereas nouns such as Disney make use of individual variables such as ya. The restriction that all expressions are of type Ind × Event → Bool simplifies the type system considerably. While it leads to difficulty with some linguistic constructions—see Section 3.3 for some examples—we believe the simplicity and robustness of the resulting system outweighs these concerns. It also leads to some spurious variables that are bound by lambdas or existentials, but which do not appear as arguments of any predicate: for example in the above analysis for Disney acquired Pixar, the variables xa, ye and ze are unused. However these “spurious” vari- ables are easily identified and discarded. An important motivation for having variables of type Ind×Event is that a single lexical item some- times makes use of both types of variables. For exam- ple, the noun phrase president in 2009 has semantics λx.∃y. president(xa) ∧ president event(xe)∧ arg1(xe,xa) ∧ 2009(ya) ∧ prep.in(xe,ya) In this example president introduces the predi- cates president, corresponding to an individual, and president event, corresponding to an event; essen- tially a presidency event that may have various prop- erties. This follows the structure of Freebase closely: 128 Freebase contains an individual corresponding to Barack Obama, with a president property, as well as an event corresponding to the Obama presidency, with various properties such as a start and end date, a location, and so on. The entry for president is then λx. president(xa) ∧ president event(xe) ∧ arg1(xe,xa) Note that proper nouns do not introduce an event predicate, as can be seen from the entries for Disney and Pixar above. 3 Dependency Structures to Logical Forms We now describe the system used to map dependency structures to logical forms. We first give an overview of the approach, then go into detail about various linguistic constructions. 3.1 An Overview of the Approach The transformation of a dependency tree to its logical form is accomplished through a series of three steps: binarization, substitution, and composition. Below, we outline these steps, with some additional remarks. Binarization. A dependency tree is mapped to an s-expression (borrowing terminology from Lisp). For example, Disney acquired Pixar has the s-expression (nsubj (dobj acquired Pixar) Disney) Formally, an s-expression has the form (exp1 exp2 exp3), where exp1 is a dependency label, and both exp2 and exp3 are either (1) a word such as acquired ; or (2) an s-expression such as (dobj acquired Pixar). We refer to the process of mapping a dependency tree to an s-expression as binarization, as it involves an ordering of modifiers to a particular head, similar to binarization of a context-free parse tree. Substitution. Each symbol (word or label) in the s-expression is assigned a lambda expression. In our running example we have the following assignments: acquired ⇒ λx. acquired(xe) Disney ⇒ λy. Disney(ya) Pixar ⇒ λz. Pixar(za) nsubj ⇒ λfgz.∃x.f(z) ∧g(x) ∧ arg1(ze,xa) dobj ⇒ λfgz.∃x.f(z) ∧g(x) ∧ arg2(ze,xa) Composition. Beta-reduction is used to compose the lambda-expression terms to compute the final semantics for the input sentence. In this step expres- sions of the form (exp1 exp2 exp3) are interpreted as function exp1 being applied to arguments exp2 and exp3. For example, (dobj acquired Pixar) re- ceives the following expression after composition: λz.∃x. acquired(ze) ∧ Pixar(xa) ∧ arg2(ze,xa) Obliqueness Hierarchy. The binarization stage re- quires a strict ordering on the different modifiers to each head in a dependency parse. For example, in (nsubj (dobj acquired Pixar) Disney), the dobj is attached before the nsubj. The ordering is very similar to the obliqueness hierarchy in syntactic for- malisms such as HPSG (Pollard and Sag, 1994). Type for Dependency Labels. Recall from Sec- tion 2 that every s-expression subtree receive a log- ical form of type η = Ind × Event → Bool. It follows that in any s-expression (exp1 exp2 exp3), exp1 has type η → (η → η), exp2 and exp3 both have type η, and the full expression has type η. Since each labeled dependency relation (e.g., nsubj, dobj, partmod) is associated with exp1 in connecting two s-expression subtrees, dependency labels always re- ceive expressions of type η → (η → η). Mirroring Dependency Structure. Whenever a dependency label receives an expression of the form λfgz.∃x.f(z) ∧g(x) ∧ rel(ze,xa) (1) where rel is a logical relation, the composition op- eration builds a structure that essentially mirrors the original dependency structure. For example nsubj and dobj receive expressions of this form, with rel = arg1 and rel = arg2, respectively; the final lambda expression for Disney acquired Pixar is λx.∃yz. acquired(xe) ∧ Disney(ya) ∧Pixar(za) ∧ arg1(xe,ya) ∧ arg2(xe,za) This structure is isomorphic to the original depen- dency structure: there are variables xe, ya and za corresponding to acquired, Disney and Pixar, respectively; and the sub-expressions arg1(xe,ya) and arg2(xe,za) correspond to the dependencies ac- quired → Disney and acquired → Pixar. By default we assume that the predicate argument structure is isomorphic to the dependency structure 129 and many dependency labels receive a semantics of the form shown in (1). However, there are a num- ber of important exceptions. As one example, the dependency label partmod receives semantics λfgz.∃x.f(z) ∧g(x) ∧ arg1(xe,za) with arg1(xe,za) in place of the arg1(ze,xa) in (1). This reverses the dependency direction to capture the predicate-argument structure of reduced relative constructions such as a company acquired by Disney. Post-processing. We apply three post-processing steps—simple inferences over lambda-calculus expressions—to the derived logical forms. These relate to the handling of prepositions, coordination and control and are described and motivated in more detail under the respective headings below. 3.2 Analysis of Some Linguistic Constructions In this section we describe in detail how various lin- guistic constructions not covered by the rule in (1)— prepositional phrases, conjunction, relative clauses, and Wh questions—are handled in the formalism.2 Prepositional Phrases. Prepositional phrase mod- ifiers to nouns and verbs have similar s-expressions: (prep president (pobj in 2009)) (prep acquired (pobj in 2009)) The following entries are used in these examples: in ⇒ λx. in(xe) prep ⇒ λfgz.∃x.f(z) ∧g(x) ∧ prep(ze,xa) pobj ⇒ λfgz.∃x.f(z) ∧g(x) ∧ pobj(ze,xa) president ⇒ λx. president(xa) ∧president event(xe) ∧ arg1(xe,xa) acquired ⇒ λx. acquired(xe) where the entries for prep and pobj simply mirror the original dependency structure with prep modifying the event variable ze. The semantics for acquired in 2009 is as follows: λx.∃py. acquired(xe) ∧ 2009(ya) ∧ in(pe) ∧ prep(xe,pe) ∧ pobj(pe,ya) 2The system contains 32 binarization rules (e.g., rules for obliqueness hierarchy and identifying traces) and 46 substi- tution rules (i.e., rules for dependency labels and parts of speech). The rules can be found at http://github.com/ sivareddyg/deplambda. We replace in(pe) ∧ prep(xe,pe) ∧ pobj(pe,ya) by prep.in(xe,ya) as a post-processing step, effectively collapsing out the p variable while replacing the prep and pobj dependencies by a single dependency, prep.in. The final semantics are then as follows: λx.∃y. acquired(xe) ∧ 2009(ya) ∧ prep.in(xe,ya) In practice this step is easily achieved by identifying variables (in this case pe) participating in prep and pobj relations. It would be tempting to achieve this step within the lambda calculus expressions them- selves, but we have found the post-processing step to be more robust to parsing errors and corner cases in the usage of the prep and pobj dependency labels. Conjunctions. First consider a simple case of NP- conjunction, Bill and Dave founded HP, whose s-expression is as follows: (nsubj (dobj founded HP) (conj-np (cc Bill and) Dave)) We make use of the following entries: conj-np ⇒ λfgx.∃yz.f(y) ∧g(z) ∧ coord(x,y,z) cc ⇒ λfgz.f(z) The sentence Bill and Dave founded HP then re- ceives the following semantics: λe.∃xyzu. Bill(ya) ∧ Dave(za) ∧ founded(ee) ∧ HP(ua) ∧coord(x,y,z) ∧ arg1(ee,xa) ∧ arg2(ee,ua) Note how the x variable occurs in two sub- expressions: coord(x,y,z), and arg1(ee,xa). It can be interpreted as a variable that conjoins variables y and z together. In particular, we introduce a post-processing step where the sub- expression coord(x,y,z) ∧ arg1(ee,xa) is replaced with arg1(ee,ya) ∧ arg1(ee,za), and the x variable is removed. The resulting expression is as follows: λe.∃yzu. Bill(ya) ∧ Dave(za) ∧ founded(ee) ∧ HP(ua) ∧arg1(ee,ya) ∧ arg1(ee,za) ∧ arg2(ee,ua) VP-coordination is treated in a very similar way. Consider the sentence Eminem signed to Interscope and discovered 50 Cent. This has the following s-expression: (nsubj (conj-vp (cc s-to-I and) d-50) Eminem) where s-to-I refers to the VP signed to Interscope, and d-50 refers to the VP discovered 50 Cent. The lambda-calculus expression for conj-vp is identical to the expression for conj-np: 130 http://github.com/sivareddyg/deplambda http://github.com/sivareddyg/deplambda conj-vp ⇒ λfgx.∃yz.f(y) ∧g(z) ∧ coord(x,y,z) The logical form for the full sentence is then λe.∃xyz. Eminem(xa) ∧ coord(e,y,z) ∧arg1(ee,xa) ∧ s to I(y) ∧ d 50(z) where we use s to I(y) and d 50(z) as shorthand for the lambda-calculus expressions for the two VPs. After post-processing this is simplified to λe.∃xyz. Eminem(xa) ∧ arg1(ye,xa) ∧arg1(ze,xa) ∧ s to I(y) ∧ d 50(z) Other types of coordination, such as sentence- level coordination and PP coordination, are handled with the same mechanism. All coordination depen- dency labels have the same semantics as conj-np and conj-vp. The only reason for having distinct de- pendency labels for different types of coordination is that different labels appear in different positions in the obliqueness hierarchy. This is important for getting the correct scope for different forms of con- junction. For instance, the following s-expression for the Eminem example would lead to an incorrect semantics: (conj-vp (nsubj (cc s-to-I and) Eminem) d-50) This s-expression is not possible under the oblique- ness hierarchy, which places nsubj modifiers to a verb after conj-vp modifiers. We realize that this treatment of conjunction is quite naive in comparison to that on offer in CCG. However, given the crude analysis of conjunction in dependency syntax, a more refined treatment is beyond the scope of the current approach. Relative Clauses. Our treatment of relative clauses is closely related to the mechanism for traces de- scribed by Moortgat (1988; 1991); see also Carpenter (1998) and Pereira (1990). Consider the NP Apple which Jobs founded with s-expression: (rcmod Apple (wh-dobj (BIND f (nsubj (dobj founded f) Jobs)) which)) Note that the s-expression has been augmented to include a variable f in dobj position, with (BIND f ...) binding this variable at the clause level. These annotations are added using a set of heuristic rules over the original dependency parse tree. The BIND operation is interpreted in the following way. If we have an expression of the form (BIND f λx.g(x)) where f is a variable and g is an expression that includes f, this is converted to λz.∃x.g(x) |f=EQ(z) where g(x) |f=EQ(z) is the expression g(x) with the expression EQ(z) substituted for f. EQ(z)(z′) is true iff z and z′ are equal (refer to the same entity). In addition we assume the following entries: wh-dobj ⇒ λfgz.f(z) rcmod ⇒ λfgz.f(z) ∧g(z) It can be verified that (BIND f (nsubj (dobj founded f) Jobs)) has semantics λu.∃xyz. founded(xe) ∧ Jobs(ya) ∧ EQ(u)(z) ∧arg1(xe,ya) ∧ arg2(xe,za) and Apple which Jobs founded has semantics λu.∃xyz. founded(xe) ∧ Jobs(ya) ∧ EQ(u)(z) ∧arg1(xe,ya) ∧ arg2(xe,za) ∧ Apple(ua) as intended. Note that this latter expression can be simplified, by elimination of the z variable, to λu.∃xy. founded(xe) ∧ Jobs(ya) ∧arg1(xe,ya) ∧ arg2(xe,ua) ∧ Apple(ua) Wh Questions. Wh questions are handled using the BIND-mechanism described in the previous sec- tion. As one example, the s-expression for Who did Jim marry is as follows: (wh-dobj (BIND f (nsubj (aux (dobj marry f) did) Jim)) who) We assume the following lambda expressions: Who ⇒ λx. TARGET(xa) did ⇒ λx. TRUE aux ⇒ λfg.f wh-dobj ⇒ λfgx.f(x) ∧g(x) It can be verified that this gives the final logical form λx.∃yz. TARGET(xa) ∧ marry(ye) ∧ Jim(za) ∧arg1(ye,za) ∧ arg2(ye,xa) Note that the predicate TARGET is applied to the variable that is the focus of the question. A similar treatment is used for cases with the wh-element in subject position (e.g., who married Jim ) or where the wh-element is extracted from a prepositional phrase (e.g., who was Jim married to ). 131 3.3 Comparison to CCG In this section we discuss some differences between our approach and CCG-based approaches for map- ping sentences to logical forms. Although our focus is on CCG, the arguments are similar for other for- malisms that use the lambda calculus in conjunction with a generative grammar, such as HPSG and LFG, or approaches based on context-free grammars. Our approach differs in two important (and re- lated) respects from CCG: (1) all constituents in our approach have the same semantic type (Ind × Event → Bool); (2) our formalism does not make the argument/adjunct distinction, instead essentially treating all modifiers to a given head as adjuncts. As an example, consider the analysis of Disney acquired Pixar within CCG. In this case acquired would be assigned the following CCG lexical entry: S\NP/NP ⇒ λf2f1x.∃yz. acquired(x) ∧f1(y) ∧f2(z) ∧arg1(x,y) ∧ arg2(x,z) Note the explicit arguments corresponding to the subject and object of this transitive verb (f1 and f2, respectively). An intransitive verb such as sleeps would be assigned an entry with a single functional argument corresponding to the subject (f1): S\NP ⇒ λf1x.∃y. sleeps(x) ∧f1(y) ∧ arg1(x,y) In contrast, the entries in our system for these two verbs are simply λx. acquired(xe) and λx. sleeps(xe). The two forms are similar, have the same semantic type, and do not include variables such as f1 and f2 for the subject and object. The advantage of our approach is that it is ro- bust, and relatively simple, in that a strict gram- mar that enforces type checking is not required. However, there are challenges in handling some lin- guistic constructions. A simple example is passive verbs. In our formalism, the passive form of ac- quired has the form λx. acquired.pass(xe), distinct from its active form λx. acquired(xe). The sen- tence Pixar was acquired is then assigned the log- ical form λx.∃y. acquired.pass(xe) ∧ Pixar(ya) ∧ arg1(xe,ya). Modifying our approach to give the same logical forms for active and passive forms would require a significant extension of our approach. In contrast, in CCG the lexical entry for the passive form of acquired can directly specify the mapping between subject position and the arg2: S\NP ⇒ λf2x.∃z. acquired(x) ∧f2(z) ∧ arg2(x,z) As another example, correct handling of object and subject control verbs is challenging in the single- type system: for example, in the analysis for John persuaded Jim to acquire Apple, the CCG analysis would have an entry for persuaded that explicitly takes three arguments (in this case John, Jim, and to acquire Apple ) and assigns Jim as both the direct object of persuaded and as the subject of acquire. In our approach the subject relationship to acquire is instead recovered in a post-processing step, based on the lexical identity of persuaded. 4 Semantic Parsing as Graph Matching We next describe how the ungrounded logical forms from the previous section are mapped to a fully grounded semantic representation that can be used for question answering against Freebase. Follow- ing Reddy et al. (2014), we treat this mapping as a graph matching problem, but instead of deriving un- grounded graphs from CCG-based logical forms, we use the dependency-based logical forms from the pre- vious sections. To learn the mapping to Freebase, we rely on manually assembled question-answer pairs. For each training question, we first find the set of oracle grounded graphs—Freebase subgraphs which when executed yield the correct answer—derivable from the question logical form. These oracle graphs are then used to train a structured perceptron model. 4.1 Ungrounded Graphs We follow Reddy et al. (2014) and first convert logi- cal forms to their corresponding ungrounded graphs. Figure 2(a) shows an example for What is the name of the company which Disney acquired in 2006?. Predi- cates corresponding to resolved entities (Disney(ya) and 2006(va)) become entity nodes (rectangles), whereas remaining entity predicates (name(wa) and company(xa)) become entity nodes (wa and xa), connected to entity type nodes (name and company; rounded rectangles). The TARGET(wa) node (dia- mond) connects to the entity node whose denotation corresponds to the answer to the question. 4.2 Grounded Graphs The ungrounded graphs are grounded to Freebase subgraphs by mapping entity nodes, entity-entity 132 name target company wa we xa ze Disney ze ze 2006 ac qu ire d. ar g1 ac qu ire d. ar g2 a c q u ire d .p re p .in a c q u ire d .a rg 2 acquired.arg 1 acquired.prep.in name.arg1 name.prep.of ty p e ty p e contract (a) Before CONTRACT. target organization. organization company name xa ze Disney ze ze 2006 ac qu ire d. ar g1 ac qu ire d. ar g2 bu sin es s. ac qu ist ion . ac qu iri ng co m pa ny bu sin ess .ac qu ist ion . co mp an y a cq uir ed a c q u ire d .p re p .in a c q u ire d .a rg 2 b u sin e ss. a c q u isitio n . d a te b u sin e ss. a c q u istio n . c o m p a n y a c q u ire d acquired.arg 1 acquired.prep.in business. acquistion. acquiring com pany business. acquisition. date type ty p e (b) After CONTRACT. Figure 2: The CONTRACT operation applied to the un- grounded graph for the question What is the name of the company which Disney acquired in 2006?. After CON- TRACT has been applied the graph is isomorphic to the representation in Freebase; in (b) we show the Freebase predicates after grounding in blue. edges and entity type nodes in the ungrounded graph to Freebase entities, relations and types, respec- tively. While Reddy et al. (2014) assume that the un- grounded graphs are isomorphic to their correspond- ing Freebase subgraph, at least 15% of the examples in our development set do not satisfy this property. For example, the ungrounded graph in Figure 2(a) is not isomorphic to the Freebase subgraph in Fig- ure 2(b), making it impossible to derive the correct grounded graph from the ungrounded one by a direct mapping. To account for such structural mismatch, we introduce two simple transformation operations. CONTRACT. The CONTRACT operation takes a pair of entity nodes connected by an edge and merges them into a single node. For example, in Figure 2(a) the entity nodes wa and xa are connected by an edge via the event we. After applying the CONTRACT op- eration to nodes wa and xa, they are merged. Note how in Figure 2(b) all the nodes attached to wa attach to the node xa after this operation. The contracted graph is now isomorphic to its Freebase subgraph. EXPAND. Parse errors may lead to ungrounded graphs with disconnected components. For example, the ungrammatical question What to do Washington DC December? results in the lambda expression λz.∃xyw. TARGET(xa) ∧ do(ze) ∧ arg1(ze,xa) ∧ Washington DC(ya) ∧ December(wa). The corre- sponding ungrounded graph has three disconnected components (December and Washington DC, and the component with entity node xa linked to event ze). In such cases, the graph is expanded by link- ing disconnected entity nodes to the event node with the largest edge degree. In the example above, this would add edges corresponding to the predicates dep(ze,ya) ∧ dep(ze,wa), where dep is the predi- cate introduced by the EXPAND operation when link- ing ya and wa to ze. When there is no existing event node in the graph, a dummy event node is introduced. 4.3 Learning We use a linear model to map ungrounded to grounded graphs. The parameters of the model are learned from question-answer pairs. For example, the question What is the name of the company which Disney acquired in 2006? is paired with its answer {Pixar}. In line with most work on question answer- ing against Freebase, we do not rely on annotated log- ical forms associated with the question for training, instead treating grounded graphs as latent variables. Let q be a question, let u be an ungrounded graph for q and let g be a grounded graph formed by ground- ing the nodes and edges of u to the knowledge base K (throughout we use Freebase as the knowledge base). Following Reddy et al. (2014), we use beam search to find the highest scoring pair of ungrounded and grounded graphs (û, ĝ) under the model θ ∈ 0.0 for training. 5 Experimental Setup We next verify empirically that our proposed ap- proach derives a useful logical compositional seman- tic representation from dependency syntax. Below, we give details on the evaluation datasets and base- lines used for comparison. We also describe the model features and provide implementation details. 5.1 Training and Evaluation Datasets We evaluated our approach on the Free917 (Cai and Yates, 2013) and WebQuestions (Berant et al., 2013) datasets. Free917 consists of 917 questions manually annotated with their Freebase query. We retrieved the answer to each question by executing its query on Freebase and ignore the query for all subsequent ex- periments. WebQuestions consists of 5810 question- answer pairs. The standard train/test splits were used for both datasets, with Free917 containing 641 train and 276 test questions and WebQuestions contain- ing 3030 train and 2780 test questions. For all our development experiments we tuned the models on held-out data consisting of 30% of the training ques- tions, while for final testing we used the complete training data. 5.2 Baseline Models and Representations In addition to the dependency-based semantic rep- resentation DEPLAMBDA (Section 3) and previous work on these datasets, we compare to three addi- tional baseline representations outlined below. We use GRAPHPARSER4 to map these representations to Freebase. DEPTREE. In this baseline, an ungrounded graph is created directly from the original dependency tree. An event is created for each parent and its dependents in the tree. Each dependent is linked to this event with an edge labeled with its dependency relation, while the parent is linked to the event with an edge labeled arg0. If a word is a question word, an additional TARGET predicate is attached to its entity node. SIMPLEGRAPH. This representation has a single event to which all entities in the question are con- nected by the predicate arg1. An additional TARGET node is connected to the event by the predicate arg0. This is similar to the template representation of Yao (2015) and Bast and Haussmann (2015). Note that this cannot represent any compositional structure. CCGGRAPH. Finally, we compare to the CCG- based semantic representation of Reddy et al. (2014), adding the CONTRACT and EXPAND operations to increase its expressivity. 5.3 Implementation Details Below are more details of our entity resolution model, the syntactic parser used, features in the grounding model and the beam search procedure. Entity Resolution. For Free917, we follow prior work and resolve entities by string match against the entity lexicon provided with the dataset. For Web- Questions, we use eight handcrafted part-of-speech patterns to identify entity span candidates. We use the Stanford CoreNLP caseless tagger for part-of-speech tagging (Manning et al., 2014). For each candidate mention span, we retrieve the top 10 entities accord- ing to the Freebase API.5 We then create a lattice in which the nodes correspond to mention-entity pairs, scored by their Freebase API scores, and the edges encode the fact that no joint assignment of entities to mentions can contain overlapping spans. Finally, we generate ungrounded graphs for the top 10 paths through the lattice and treat the final entity disam- biguation as part of the semantic parsing problem. 4 http://github.com/sivareddyg/graph-parser 5 http://developers.google.com/freebase/ 134 http://github.com/sivareddyg/graph-parser http://developers.google.com/freebase/ Representation -C -E -C +E +C -E +C +E (a) Average oracle F1 DEPTREE 30.8 30.8 72.8 72.8 SIMPLEGRAPH 73.0 73.0 73.0 73.0 CCGGRAPH 65.1 70.3 67.6 72.9 DEPLAMBDA 64.8 66.3 71.8 73.0 (b) Average number of oracle graphs per question DEPTREE 1.5 1.5 354.6 354.6 SIMPLEGRAPH 1.5 1.5 1.8 1.8 CCGGRAPH 1.6 1.7 3.4 3.4 DEPLAMBDA 1.4 1.5 3.6 4.2 (c) Average F1 DEPTREE 19.9 19.9 42.6 42.6 SIMPLEGRAPH 49.0 49.0 48.2 48.2 CCGGRAPH 44.7 47.3 46.5 48.9 DEPLAMBDA 45.9 47.5 48.8 50.4 Table 1: Oracle statistics and accuracies on the Web- Questions development set. +(-)C: with(out) CONTRACT. +(-)E: with(out) EXPAND. Syntactic Parsing. We recase the resolved entity mentions and run a case-sensitive second-order con- ditional random field part-of-speech tagger (Laf- ferty et al., 2001). The hypergraph parser of Zhang and McDonald (2014) is used for dependency pars- ing. The tagger and parser are both trained on the OntoNotes 5.0 corpus (Weischedel et al., 2011), with constituency trees converted to Stanford-style depen- dencies (De Marneffe and Manning, 2008). To derive the CCG-based representation, we use the output of the EasyCCG parser (Lewis and Steedman, 2014). Features. We use the features from Reddy et al. (2014), which include edge alignment and stem over- lap between ungrounded and grounded graphs, and contextual features such as word and grounded rela- tion pairs. In addition, we introduce a feature indi- cating the use of the CONTRACT operation: (Merged- SubEdge, HeadSubEdge, MergedIsEntity, HeadIsEn- tity). For example, in Figure 2 the edge between wa and xa is contracted to xa, resulting in the feature (name.arg1, name.prep.of, False, False). The EX- PAND operation is treated as a pre-processing step and no features are used to encode its use. Finally, the entity-lattice score is used as a real valued feature. Beam Search. We use beam search to infer the highest scoring graph pair for a question. The search operates over entity-entity edges and entity type nodes of each ungrounded graph. For an entity-entity Representation -C -E -C +E +C -E +C +E (a) Oracle Accuracy DEPTREE 26.0 26.0 95.8 95.8 SIMPLEGRAPH 96.3 96.3 96.3 96.3 CCGGRAPH 91.2 93.3 92.2 95.3 DEPLAMBDA 91.1 92.7 94.3 95.8 (b) Average number of oracle graphs per question DEPTREE 1.2 1.2 285.4 285.4 SIMPLEGRAPH 1.6 1.6 1.8 1.8 CCGGRAPH 1.6 1.6 2.4 2.5 DEPLAMBDA 1.5 1.5 3.3 3.4 (c) Accuracy DEPTREE 21.3 21.3 51.6 51.6 SIMPLEGRAPH 40.9 40.9 42.0 42.0 CCGGRAPH 68.3 69.4 70.4 71.0 DEPLAMBDA 69.3 71.3 72.4 73.4 Table 2: Oracle statistics and accuracies on the Free917 development set. +(-)C: with(out) CONTRACT. +(-)E: with(out) EXPAND. edge, we can ground the edge to a Freebase relation, contract the edge in either direction, or skip the edge. For an entity type node, we can ground the node to a Freebase type, or skip the node. The order of traversal is based on the number of named entities connected to an edge. After an edge is grounded, the entity type nodes connected to it are grounded in turn, before the next edge is processed. To restrict the search, if two beam items correspond to the same grounded graph, the one with the lower score is discarded. A beam size of 100 was used in all experiments. 6 Experimental Results We examine the different representations for ques- tion answering along two axes. First, we compare their expressiveness in terms of answer reachability assuming a perfect model. Second, we compare their performance with a learned model. Finally, we con- duct a detailed error analysis of DEPLAMBDA, with a comparison to the errors made by CCGGRAPH. For WebQuestions evaluation is in terms of the av- erage F1-score across questions, while for Free917, evaluation is in terms of exact answer accuracy.6 6.1 Expressiveness of the Representations Table 1(a) and Table 2(a) show the oracle F1-scores of each representation on the WebQuestions and 6We use the evaluation scripts available at http:// www-nlp.stanford.edu/software/sempre and http:// github.com/elmar-haussmann/aqqu, respectively. 135 http://www-nlp.stanford.edu/software/sempre http://www-nlp.stanford.edu/software/sempre http://github.com/elmar-haussmann/aqqu http://github.com/elmar-haussmann/aqqu Free917 development sets respectively. According to the first column (-C -E), the original DEPTREE repre- sentation can be directly mapped to Freebase for less than a third of the questions. Adding the CONTRACT operation (+C) improves this substantially to an ora- cle F1 of about 73% on WebQuestions and 95.8% on Free917. However, this comes at the cost of massive spurious ambiguity: from Table 1(b) there are on av- erage over 300 oracle graphs for a single dependency tree. Table 1(c) shows the results of the different representations on the WebQuestions development set. Spurious ambiguity clearly hampers learning and DEPTREE falls behind the other representations. CCGGRAPH and DEPLAMBDA align much more closely to Freebase and achieve similar oracle F1 scores with far less spurious ambiguity. SIMPLE- GRAPH, which cannot represent any compositional semantics, is competitive with these syntax-based representations. This might come as a surprise, but it simply reflects the fact that the dataset does not con- tain questions that require compositional reasoning. 6.2 Results on WebQuestions and Free917 We use the best settings on the development set in subsequent experiments, i.e., with CONTRACT and EXPAND enabled. Table 3 shows the results on the WebQuestions and Free917 test sets with additional entries for recent prior work on these datasets. The trend from the development set carries over and DE- PLAMBDA outperforms the other graph-based repre- sentations, while performing slightly below the state- of-the-art model of Yih et al. (2015) (“Y&C”), which uses a separately trained entity resolution system (Yang and Chang, 2015). When using the standard Freebase API (“FB API”) for entity resolution, the performance of their model drops to 48.4% F1. On Free917, DEPLAMBDA outperforms all other representations by a wide margin and obtains the best result to date. Interestingly, DEPTREE outperforms SIMPLEGRAPH in this case. We attribute this to the small training set and larger lexical variation of Free917. The structural features of the graph-based representations seem highly beneficial in this case. 6.3 Error Analysis We categorized 100 errors made by DEPLAMBDA (+C +E) on the WebQuestions development set. In 43 cases the correct answer is present in the beam, Free917 WebQuestions Method Accuracy Average F1 Cai and Yates (2013) 59.0 – Berant et al. (2013) 62.0 35.7 Kwiatkowski et al. (2013) 68.0 – Yao and Van Durme (2014) – 33.0 Berant and Liang (2014) 68.5 39.9 Bao et al. (2014) – 37.5 Bordes et al. (2014) – 39.2 Yao (2015) – 44.3 Yih et al. (2015) (FB API) – 48.4 Bast and Haussmann (2015) 76.4 49.4 Berant and Liang (2015) – 49.7 Yih et al. (2015) (Y&C) – 52.5 This Work DEPTREE 53.2 40.4 SIMPLEGRAPH 43.7 48.5 CCGGRAPH (+C +E) 73.3 48.6 DEPLAMBDA (+C +E) 78.0 50.3 Table 3: Question-answering results on the WebQuestions and Free917 test sets. but ranked below an incorrect answer (e.g., for where does volga river start, the annotated gold answer is Valdai Hills, which is ranked second, with Russia, Europe ranked first). In 35 cases, only a subset of the answer is predicted correctly (e.g, for what coun- tries in the world speak german, the system predicts Germany from the human language.main country Freebase relation, whereas the gold relation human language.countries spoken in gives multi- ple countries). Together, these two categories corre- spond to roughly 80% of the errors. In 10 cases, the Freebase API fails to add the gold entity to the lattice (e.g., for who is blackwell, the correct blackwell en- tity was missing). Due to the way WebQuestions was crowdsourced, 9 questions have incorrect or incom- plete gold annotations (e.g., what does each fold of us flag means is answered with USA). The remaining 3 cases are due to structural mismatch (e.g., in who is the new governor of florida 2011, the graph failed to connect the target node with both 2011 and Florida ). Due to the ungrammatical nature of WebQuestions, CCGGRAPH fails to produce ungrounded graphs for 4.5% of the complete development set, while DE- PLAMBDA is more robust with only 0.9% such errors. The CCG parser is restricted to produce a sentence tag as the final category in the syntactic derivation, which penalizes ungrammatical analyses (e.g., what 136 victoria beckham kids names and what nestle owns ). Examples where DEPLAMBDA fails due to parse er- rors, but CCGGRAPH succeed include when was blessed kateri born and where did anne frank live before the war. Note that the EXPAND operation mit- igates some of these problems. While CCG is known for handling comparatives elegantly (e.g., who was sworn into office when john f kennedy was assassi- nated ), we do not have a special treatment for them in the semantic representation. Differences in syn- tactic parsing performance and the somewhat limited expressivity of the semantic representation are likely the reasons for CCGGRAPH’s lower performance. 7 Related Work There are two relevant strands of prior work: gen- eral purpose ungrounded semantics and grounded semantic parsing. The former have been studied on their own and as a component in tasks such as seman- tic parsing to knowledge bases (Kwiatkowski et al., 2013; Reddy et al., 2014; Choi et al., 2015; Krishna- murthy and Mitchell, 2015), sentence simplification (Narayan and Gardent, 2014), summarization (Liu et al., 2015), paraphrasing (Pavlick et al., 2015) and relation extraction (Rocktäschel et al., 2015). There are two ways of generating these representations: ei- ther relying on syntactic structure and producing the semantics post hoc, or generating it directly from text. We adopt the former approach, which was pioneered by Montague (1973) and is becoming increasingly at- tractive with the advent of accurate syntactic parsers. There have been extensive studies on extracting semantics from syntactic representations such as LFG (Dalrymple et al., 1995), HPSG (Copestake et al., 2001; Copestake et al., 2005), TAG (Gar- dent and Kallmeyer, 2003; Joshi et al., 2007) and CCG (Baldridge and Kruijff, 2002; Bos et al., 2004; Steedman, 2012; Artzi et al., 2015). However, few have used dependency structures for this purpose. Debusmann et al. (2004) and Cimiano (2009) de- scribe grammar-based conversions of dependencies to semantic representations, but do not validate them empirically. Stanovsky et al. (2016) use heuristics based on linguistic grounds to convert dependen- cies to proposition structures. Bédaride and Gar- dent (2011) propose a graph-rewriting technique to convert a graph built from dependency trees and se- mantic role structures to a first-order logical form, and present results on textual entailment. Our work, in contrast, assumes access only to dependency trees and offers an alternative method based on the lambda calculus, mimicking the structure of knowledge bases such as Freebase; we further present extensive empir- ical results on recent question-answering corpora. Structural mismatch between the source semantic representation and the target application’s represen- tation is an inherent problem with approaches using general-purpose representations. Kwiatkowski et al. (2013) propose lambda-calculus operations to gen- erate multiple type-equivalent expressions to handle this mismatch. In contrast, we use graph-transduction operations which are relatively easier to interpret. There is also growing work on converting syntactic structures to the target application’s structure without going through an intermediate semantic representa- tion, e.g., answer-sentence selection (Punyakanok et al., 2004; Heilman and Smith, 2010; Yao et al., 2013) and semantic parsing (Ge and Mooney, 2009; Poon, 2013; Parikh et al., 2015; Xu et al., 2015; Wang et al., 2015; Andreas and Klein, 2015). A different paradigm is to directly parse the text into a grounded semantic representation. Typically, an over-generating grammar is used whose accepted parses are ranked (Zelle and Mooney, 1996; Zettle- moyer and Collins, 2005; Wong and Mooney, 2007; Kwiatkowksi et al., 2010; Liang et al., 2011; Berant et al., 2013; Flanigan et al., 2014; Groschwitz et al., 2015). In contrast, Bordes et al. (2014) and Dong et al. (2015) discard the notion of a target represen- tation altogether and instead learn to rank potential answers to a given question by embedding questions and answers into the same vector space. 8 Conclusion We have introduced a method for converting depen- dency structures to logical forms using the lambda calculus. A key idea of this work is the use of a single semantic type for every constituent of the dependency tree, which provides us with a robust way of com- positionally deriving logical forms. The resulting representation is subsequently grounded to Freebase by learning from question-answer pairs. Empirically, the proposed representation was shown to be superior to the original dependency trees and more robust than logical forms derived from a CCG parser. 137 Acknowledgements This work greatly benefitted from discussions with Slav Petrov, John Blitzer, Fernando Pereira, Emily Pitler and Nathan Schneider. The authors would also like to thank Christopher Potts and the three anony- mous reviewers for their valuable feedback. We ac- knowledge the financial support of EU IST Cognitive Systems IP EC-FP7-270273 “Xperience” (Steedman) and EPSRC (EP/K017845/1) in the framework of the CHIST-ERA READERS project (Lapata). References Jacob Andreas and Dan Klein. 2015. Alignment-Based Compositional Semantics for Instruction Following. In Proceedings of Empirical Methods on Natural Lan- guage Processing, pages 1165–1174. Yoav Artzi, Kenton Lee, and Luke Zettlemoyer. 2015. Broad-coverage CCG Semantic Parsing with AMR. In Proceedings of Empirical Methods on Natural Lan- guage Processing, pages 1699–1710. Jason Baldridge and Geert-Jan Kruijff. 2002. Coupling CCG and Hybrid Logic Dependency Semantics. In Pro- ceedings of Association for Computational Linguistics, pages 319–326. Junwei Bao, Nan Duan, Ming Zhou, and Tiejun Zhao. 2014. Knowledge-Based Question Answering as Ma- chine Translation. In Proceedings of Association for Computational Linguistics, pages 967–976. Hannah Bast and Elmar Haussmann. 2015. More Accu- rate Question Answering on Freebase. In Proceedings of ACM International Conference on Information and Knowledge Management, pages 1431–1440. Paul Bédaride and Claire Gardent. 2011. Deep Semantics for Dependency Structures. In Proceedings of Confer- ence on Intelligent Text Processing and Computational Linguistics, pages 277–288. Jonathan Berant and Percy Liang. 2014. Semantic Parsing via Paraphrasing. In Proceedings of Association for Computational Linguistics, pages 1415–1425. Jonathan Berant and Percy Liang. 2015. Imitation Learning of Agenda-Based Semantic Parsers. Transac- tions of the Association for Computational Linguistics, 3:545–558. Jonathan Berant, Andrew Chou, Roy Frostig, and Percy Liang. 2013. Semantic Parsing on Freebase from Question-Answer Pairs. In Proceedings of Empirical Methods on Natural Language Processing, pages 1533– 1544. Antoine Bordes, Sumit Chopra, and Jason Weston. 2014. Question Answering with Subgraph Embeddings. In Proceedings of Empirical Methods on Natural Lan- guage Processing, pages 615–620. Johan Bos, Stephen Clark, Mark Steedman, James R. Cur- ran, and Julia Hockenmaier. 2004. Wide-Coverage Semantic Representations from a CCG Parser. In Pro- ceedings of International Conference on Computational Linguistics, pages 1240–1246. Qingqing Cai and Alexander Yates. 2013. Large-scale Semantic Parsing via Schema Matching and Lexicon Extension. In Proceedings of Association for Computa- tional Linguistics, pages 423–433. Bob Carpenter. 1998. Type-Logical Semantics. MIT Press, Cambridge, MA, USA. David L. Chen and Raymond J. Mooney. 2011. Learning to Interpret Natural Language Navigation Instructions from Observations. In Proceedings of Association for the Advancement of Artificial Intelligence, pages 1–2. Eunsol Choi, Tom Kwiatkowski, and Luke Zettlemoyer. 2015. Scalable Semantic Parsing with Partial Ontolo- gies. In Proceedings of Association for Computational Linguistics, pages 1311–1320. Philipp Cimiano. 2009. Flexible Semantic Composition with DUDES. In Proceedings of International Confer- ence on Computational Semantics, pages 272–276. Michael Collins. 2002. Discriminative Training Methods for Hidden Markov Models: Theory and Experiments with Perceptron Algorithms. In Proceedings of Empiri- cal Methods on Natural Language Processing, pages 1–8. Ann Copestake, Alex Lascarides, and Dan Flickinger. 2001. An Algebra for Semantic Construction in Constraint-based Grammars. In Proceedings of Associ- ation for Computational Linguistics, pages 140–147. Ann Copestake, Dan Flickinger, Carl Pollard, and Ivan A. Sag. 2005. Minimal Recursion Semantics: An In- troduction. Research on Language and Computation, 3(2-3):281–332. Mary Dalrymple, John Lamping, Fernando C. N. Pereira, and Vijay A. Saraswat. 1995. Linear Logic for Mean- ing Assembly. In Proceedings of Computational Logic for Natural Language Processing. Marie-Catherine De Marneffe and Christopher D Manning. 2008. Stanford typed dependencies manual. Technical report, Stanford University. Ralph Debusmann, Denys Duchier, Alexander Koller, Marco Kuhlmann, Gert Smolka, and Stefan Thater. 2004. A Relational Syntax-Semantics Interface Based on Dependency Grammar. In Proceedings of Interna- tional Conference on Computational Linguistics, pages 176–182. Li Dong, Furu Wei, Ming Zhou, and Ke Xu. 2015. Ques- tion Answering over Freebase with Multi-Column Con- volutional Neural Networks. In Proceedings of Associ- ation for Computational Linguistics, pages 260–269. 138 Jeffrey Flanigan, Sam Thomson, Jaime Carbonell, Chris Dyer, and Noah A. Smith. 2014. A Discriminative Graph-Based Parser for the Abstract Meaning Repre- sentation. In Proceedings of Association for Computa- tional Linguistics, pages 1426–1436. Yoav Freund and Robert E. Schapire. 1999. Large Margin Classification Using the Perceptron Algorithm. Ma- chine Learning, 37(3):277–296, December. Claire Gardent and Laura Kallmeyer. 2003. Semantic Construction in Feature-based TAG. In Proceedings of European Chapter of the Association for Computa- tional Linguistics, pages 123–130. Ruifang Ge and Raymond Mooney. 2009. Learning a Compositional Semantic Parser using an Existing Syntactic Parser. In Proceedings of Association for Computational Linguistics, pages 611–619. Jonas Groschwitz, Alexander Koller, and Christoph Teich- mann. 2015. Graph parsing with s-graph grammars. In Proceedings of Association for Computational Linguis- tics, pages 1481–1490. Michael Heilman and Noah A. Smith. 2010. Tree Edit Models for Recognizing Textual Entailments, Para- phrases, and Answers to Questions. In Proceedings of North American Chapter of the Association for Com- putational Linguistics, pages 1011–1019. Aravind K. Joshi, Laura Kallmeyer, and Maribel Romero. 2007. Flexible Composition In LTAG: Quantifier Scope and Inverse Linking. In Harry Bunt and Reinhard Muskens, editors, Computing Meaning, volume 83 of Studies in Linguistics and Philosophy, pages 233–256. Springer Netherlands. Jayant Krishnamurthy and Tom Mitchell. 2012. Weakly Supervised Training of Semantic Parsers. In Proceed- ings of Empirical Methods on Natural Language Pro- cessing, pages 754–765. Jayant Krishnamurthy and Tom M. Mitchell. 2015. Learn- ing a Compositional Semantics for Freebase with an Open Predicate Vocabulary. Transactions of the Associ- ation for Computational Linguistics, 3:257–270. Tom Kwiatkowksi, Luke Zettlemoyer, Sharon Goldwater, and Mark Steedman. 2010. Inducing Probabilistic CCG Grammars from Logical Form with Higher-Order Unification. In Proceedings of Empirical Methods on Natural Language Processing, pages 1223–1233. Tom Kwiatkowski, Eunsol Choi, Yoav Artzi, and Luke Zettlemoyer. 2013. Scaling Semantic Parsers with On-the-Fly Ontology Matching. In Proceedings of Empirical Methods on Natural Language Processing, pages 1545–1556. John Lafferty, Andrew McCallum, and Fernando Pereira. 2001. Conditional Random Fields: Probabilistic Mod- els for Segmenting and Labeling Sequence Data. In Proceedings of International Conference on Machine Learning, pages 282–289. Mike Lewis and Mark Steedman. 2014. A* CCG Parsing with a Supertag-factored Model. In Proceedings of Empirical Methods on Natural Language Processing, pages 990–1000. Percy Liang, Michael Jordan, and Dan Klein. 2011. Learning Dependency-Based Compositional Seman- tics. In Proceedings of Association for Computational Linguistics, pages 590–599. Fei Liu, Jeffrey Flanigan, Sam Thomson, Norman Sadeh, and Noah A. Smith. 2015. Toward Abstractive Sum- marization Using Semantic Representations. In Pro- ceedings of North American Chapter of the Association for Computational Linguistics, pages 1077–1086. Christopher D. Manning, Mihai Surdeanu, John Bauer, Jenny Finkel, Steven J. Bethard, and David McClosky. 2014. The Stanford CoreNLP Natural Language Pro- cessing Toolkit. In Proceedings of Association for Com- putational Linguistics, pages 55–60. Andre Martins, Miguel Almeida, and Noah A. Smith. 2013. Turning on the Turbo: Fast Third-Order Non- Projective Turbo Parsers. In Proceedings of Associa- tion for Computational Linguistics, pages 617–622. Cynthia Matuszek, Nicholas FitzGerald, Luke Zettle- moyer, Liefeng Bo, and Dieter Fox. 2012. A Joint Model of Language and Perception for Grounded At- tribute Learning. In Proceedings of International Con- ference on Machine Learning. Ryan McDonald, Fernando Pereira, Kiril Ribarov, and Jan Hajič. 2005. Non-Projective Dependency Parsing using Spanning Tree Algorithms. In Proceedings of Empirical Methods on Natural Language Processing, pages 523–530. Richard Montague. 1973. The Proper Treatment of Quan- tification in Ordinary English. In K.J.J. Hintikka, J.M.E. Moravcsik, and P. Suppes, editors, Approaches to Nat- ural Language, volume 49 of Synthese Library, pages 221–242. Springer Netherlands. Michael Moortgat. 1988. Categorical Investigations. Log- ical and Linguistic Aspects of the Lambek Calculus. Foris, Dordrecht. Michael Moortgat. 1991. Generalized Quantification and Discontinuous Type Constructors. Technical report, University of Utrecht. Shashi Narayan and Claire Gardent. 2014. Hybrid Sim- plification using Deep Semantics and Machine Transla- tion. In Proceedings of Association for Computational Linguistics, pages 435–445. Joakim Nivre, Johan Hall, Jens Nilsson, Atanas Chanev, Gülsen Eryigit, Sandra Kübler, Svetoslav Marinov, and Erwin Marsi. 2007. MaltParser: A Language- Independent System for Data-Driven Dependency Pars- ing. Natural Language Engineering, 13(2):95–135. 139 Ankur P. Parikh, Hoifung Poon, and Kristina Toutanova. 2015. Grounded Semantic Parsing for Complex Knowl- edge Extraction. In Proceedings of North American Chapter of the Association for Computational Linguis- tics, pages 756–766. Ellie Pavlick, Johan Bos, Malvina Nissim, Charley Beller, Benjamin Van Durme, and Chris Callison-Burch. 2015. Adding Semantics to Data-Driven Paraphrasing. In Pro- ceedings of Association for Computational Linguistics, pages 1512–1522. Fernando C. N. Pereira. 1990. Categorial Semantics and Scoping. Computational Linguistics, 16(1):1–10. Carl Pollard and Ivan A. Sag. 1994. Head-Driven Phrase Structure Grammar. University of Chicago Press. Hoifung Poon. 2013. Grounded Unsupervised Semantic Parsing. In Proceedings of Association for Computa- tional Linguistics, pages 933–943. Vasin Punyakanok, Dan Roth, and Wen-tau Yih. 2004. Mapping Dependencies Trees: An Application to Ques- tion Answering. In Proceedings of International Sym- posium on Artificial Intelligence and Mathematics, pages 1–10. Siva Reddy, Mirella Lapata, and Mark Steedman. 2014. Large-scale Semantic Parsing without Question- Answer Pairs. Transactions of the Association for Com- putational Linguistics, 2:377–392. Tim Rocktäschel, Sameer Singh, and Sebastian Riedel. 2015. Injecting Logical Background Knowledge into Embeddings for Relation Extraction. In Proceedings of North American Chapter of the Association for Compu- tational Linguistics, pages 1119–1129. Gabriel Stanovsky, Jessica Ficler, Ido Dagan, and Yoav Goldberg. 2016. Getting More Out Of Syntax with PropS. ArXiv e-prints, March. Mark Steedman. 2012. Taking Scope - The Natural Se- mantics of Quantifiers. MIT Press. Chuan Wang, Nianwen Xue, and Sameer Pradhan. 2015. A Transition-based Algorithm for AMR Parsing. In Proceedings of North American Chapter of the Associ- ation for Computational Linguistics, pages 366–375. Ralph Weischedel, Eduard Hovy, Martha Palmer, Mitch Marcus, Robert Belvin, Sameer Pradhan, Lance Ramshaw, and Nianwen Xue. 2011. OntoNotes: A Large Training Corpus for Enhanced Processing. In J. Olive, C. Christianson, and J. McCary, editors, Hand- book of Natural Language Processing and Machine Translation. Springer. Yuk Wah Wong and Raymond J. Mooney. 2006. Learning for Semantic Parsing with Statistical Machine Trans- lation. In Proceedings of North American Chapter of the Association for Computational Linguistics, pages 439–446. Yuk Wah Wong and Raymond Mooney. 2007. Learn- ing Synchronous Grammars for Semantic Parsing with Lambda Calculus. In Proceedings of Association for Computational Linguistics, pages 960–967. Kun Xu, Yansong Feng, Songfang Huang, and Dongyan Zhao. 2015. Question Answering via Phrasal Semantic Parsing. In Proceedings of Conference and Labs of the Evaluation Forum, pages 414–426. Yi Yang and Ming-Wei Chang. 2015. S-MART: Novel Tree-based Structured Learning Algorithms Applied to Tweet Entity Linking. In Proceedings of Association for Computational Linguistics, pages 504–513. Xuchen Yao and Benjamin Van Durme. 2014. Informa- tion Extraction over Structured Data: Question Answer- ing with Freebase. In Proceedings of Association for Computational Linguistics, pages 956–966. Xuchen Yao, Benjamin Van Durme, Chris Callison-Burch, and Peter Clark. 2013. Answer Extraction as Sequence Tagging with Tree Edit Distance. In Proceedings of North American Chapter of the Association for Compu- tational Linguistics, pages 858–867. Xuchen Yao. 2015. Lean Question Answering over Free- base from Scratch. In Proceedings of North American Chapter of the Association for Computational Linguis- tics, pages 66–70. Wen-tau Yih, Ming-Wei Chang, Xiaodong He, and Jian- feng Gao. 2015. Semantic Parsing via Staged Query Graph Generation: Question Answering with Knowl- edge Base. In Proceedings of Association for Compu- tational Linguistics, pages 1321–1331. John M. Zelle and Raymond J. Mooney. 1996. Learning to Parse Database Queries Using Inductive Logic Pro- gramming. In Proceedings of Association for the Ad- vancement of Artificial Intelligence, pages 1050–1055. Luke S. Zettlemoyer and Michael Collins. 2005. Learning to Map Sentences to Logical Form: Structured Clas- sification with Probabilistic Categorial Grammars. In Proceedings of Uncertainty in Artificial Intelligence, pages 658–666. Hao Zhang and Ryan McDonald. 2014. Enforcing Struc- tural Diversity in Cube-pruned Dependency Parsing. In Proceedings of Association for Computational Linguis- tics, pages 656–661. 140