Abstraction and Ontology: Questions as Propositional Abstracts in Type Theory with Records

  • Authors:
  • Jonathan Ginzburg

  • Affiliations:
  • Department of Computer Science, King's College London, Strand, London WC2R 2LS, UK. E-mail: ginzburg@dcs.kcl.ac.uk

  • Venue:
  • Journal of Logic and Computation
  • Year:
  • 2005

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Abstract

The paper develops a semantics for natural language interrogatives which identifies questions---the denotations of interrogatives---with propositional abstracts. The paper argues that a theory of Questions as Propositional Abstracts (QPA), is a simple, transparently implementable theory that has significant empirical coverage. However, until recently QPA has been abandoned in formal semantic treatments of questions, due to a number of significant problems QPA encountered when formulated within the type system of Montague Semantics. In recent work, Ginzburg and Sag provided a a situation theoretic implementation of QPA that succeeded in overcoming certain of the original problems for QPA. However, Ginzburg and Sag's proposal relied on a special purpose account of λ-abstraction, raising the question to what extent QPA can be sustained using standard notions of abstraction. In this paper such doubts are allayed by implementing QPA in a version of Type Theory that provides record types. These latter allow one to develop notions of simultaneous/vacuous abstraction with restrictions and an ontology with various 'informational entities'. Moreover, the intrinsic polymorphism of this theory plays a crucial role in enabling the definition of a general type for questions, one of the main stumbling blocks for earlier versions of QPA.