NLCS'15: Papers with AbstractsPapers 

Abstract. This paper, which attempts to develop an abstract construct that generalizes the intensionalization procedure introduced by Kanazawa and de Groote, advocates for the use of logical relations in order to establish conservativity results.  Abstract. Pregroup grammars are a recent descendant of the original categorial grammars of BarHillel [1] and Lambek [10] in which types take the form of strings of basic types and left and right adjoints, as opposed to the noncommutative functional types of categorial grammars. Whereas semantic extraction is possible in other categorial grammars through the λcalculus, this approach will not be feasible for pregroup grammars. In this paper, we show how to build a term calculus that could be used to fill this void. This system is inspired by the λcalculus but differs in crucial aspects: it uses function composition as its main reduction strategy instead of function application and is bidirectional, i.e. the direction arguments are applied to terms matters. We show how this term calculus is one toone with a proper subset of pregroup types and give multiple examples to show how this system could be used to do semantic analysis in parallel to doing grammaticality checks with pregroup grammars.  Abstract. We present the grammar/semantic formalism of Applicative Abstract Categorial Grammar (AACG), based on the recent techniques from functional programming: applicative functors, staged languages and typed final language embeddings. AACG is a generalization of Abstract Categorial Grammars (ACG), retaining the benefits of ACG as a grammar formalism and making it possible and convenient to express a variety of semantic theories.
We use the AACG formalism to uniformly formulate Potts' analyses of expressives, the dynamiclogic account of anaphora, and the continuation tower treatment of quantifier strength, quantifier ambiguity and scope islands. Carrying out these analyses in ACG required compromises and the ballooning of parsing complexity, or was not possible at all. The AACG formalism brings modularity, which comes from the compositionality of applicative functors, in contrast to monads, and the extensibility of the typed final embedding. The separately developed analyses of expressives and QNP are used as they are to compute truth conditions of sentences with both these features.
AACG is implemented as a `semantic calculator', which is the ordinary Haskell interpreter. The calculator lets us interactively write grammar derivations in a linguistreadable form and see their yields, inferred types and computed truth conditions. We easily extend fragments with more lexical items and operators, and experiment with different semanticmapping assemblies. The mechanization lets a semanticist test more and more complex examples, making empirical tests of a semantic theory more extensive, organized and systematic.  Abstract. We have proposed a framework based upon the λ calculus with higherorder intuitionistic types for the symbolic computation of the semantic analysis, integrating lexical data. This proposal is sufficient for many phenomena and accurately incorporates lexical semantics by the means of type theory, but some issues linger in the linguistic data. In the present paper, we revisit this proposal with a version of the λ calculus based upon higherorder linear types, that aims to resolve those issues and present an integrated framework for meaning assembly.  Abstract. We study nonlinear connectives (exponentials) in the context of Type Logical Grammar (TLG). We devise four conservative extensions of the Displacement calculus with brackets, \DbC, \DbCM, \DbCb and \DbCbMr which contain the universal and existential exponential modalities of linear logic (\LL). These modalities do not exhibit the same structural properties as in \LL, which in TLG are especially adapted for linguistic purposes. The universal modality \univexp for TLG allows only the commutative and contraction rules, but not weakening, whereas the existential modality \exstexp allows the socalled (intuitionistic) mingle rule, which derives a restricted version of weakening called \emph{expansion}. We provide a CurryHoward labelling for both exponential connectives. As it turns out, controlled contraction by \univexp gives a way to account for the socalled parasitic gaps, and controlled Mingle \exstexp iterability, in particular iterated coordination. Finally, the four calculi are proved to be CutFree but decidability is only proved for $\DbCb$, whereas for the rest the question of decidability remains open.  Abstract. We prove that nonlinear second order Abstract Categorial Grammars (2ACGs) are equivalent to nondeleting 2ACGs. We prove this result first by using the intersection types discipline. Then we explain how coherence spaces can yield the same result. This result shows that restricting the Montagovian approach to natural language semantics to use only $\L I$terms has no impact in terms of the definable syntax/semantics relations. 

