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Intensional models for the theory of types

Published online by Cambridge University Press:  12 March 2014

Reinhard Muskens
Reinhard Muskens*
Affiliation:
Tilburg University, Department of Philosophy, P.O. Box 90153, NL 5000 LE, Tilburg, The Netherlands. E-mail: r.a.muskens@uvt.nl URL: http://let.uvt.nl/general/people/rmuskens/
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Abstract

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 98 - 118
Copyright
Copyright © Association for Symbolic Logic 2007

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