Abstraction and Ontology: Questions as Propositional Abstracts in Type Theory with Records
Jonathan Ginzburg · Journal of Logic and Computation · 2005
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.