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Continuation Semantics for Symmetric Categorial Grammar

  • Raffaella Bernardi
  • Michael Moortgat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4576)

Abstract

Categorial grammars in the tradition of Lambek [1,2] are asymmetric: sequent statements are of the form \({\Gamma}\Rightarrow{A}\), where the succedent is a single formula A, the antecedent a structured configuration of formulas A 1,...,A n . The absence of structural context in the succedent makes the analysis of a number of phenomena in natural language semantics problematic. A case in point is scope construal: the different possibilities to build an interpretation for sentences containing generalized quantifiers and related expressions. In this paper, we explore a symmetric version of categorial grammar based on work by Grishin [3]. In addition to the Lambek product, left and right division, we consider a dual family of type-forming operations: coproduct, left and right difference. Communication between the two families is established by means of structure-preserving distributivity principles. We call the resulting system LG. We present a Curry-Howard interpretation for Open image in new window derivations. Our starting point is Curien and Herbelin’s sequent system for λμ calculus [4] which capitalizes on the duality between logical implication (i.e. the Lambek divisions under the formulas-as-types perspective) and the difference operation. Importing this system into categorial grammar requires two adaptations: we restrict to the subsystem where linearity conditions are in effect, and we refine the interpretation to take the left-right symmetry and absence of associativity/commutativity into account. We discuss the continuation-passing-style (CPS) translation, comparing the call-by-value and call-by-name evaluation regimes. We show that in the latter (but not in the former) the types of LG are associated with appropriate denotational domains to enable a proper treatment of scope construal.

Keywords

Noun Phrase Sequent Calculus Type Assignment Natural Language Semantic Categorial Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Raffaella Bernardi
    • 1
  • Michael Moortgat
    • 2
  1. 1.Free University of Bozen-BolzanoItaly
  2. 2.Utrecht Institute of Linguistics OTSThe Netherlands

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