NLCS'15: Papers with Abstracts

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 Bar-Hillel [1] and Lambek [10] in which types take the form of strings of basic types and left and right adjoints, as opposed to the non-commutative functional types of categorial grammars. Whereas semantic extraction is possible in other categorial grammars through the λ-calculus, 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 λ-calculus 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- to-one 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 dynamic-logic 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 linguist-readable 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 semantic-mapping 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 higher-order 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 higher-order 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 so-called (intuitionistic) mingle rule, which
derives a restricted version of weakening called \emph{expansion}. We provide a Curry-Howard labelling for both exponential connectives. As it turns out,
controlled contraction by \univexp gives a way to account for the so-called parasitic gaps, and controlled Mingle \exstexp iterability, in particular iterated
coordination. Finally, the four calculi are proved to be Cut-Free but decidability is only proved for $\DbCb$, whereas
for the rest the question of decidability remains open.

Abstract. We prove that non-linear second order Abstract Categorial Grammars
(2ACGs) are equivalent to non-deleting 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.