Journal of Symbolic Logic 72 (1):98-118 (2007)

Authors
Reinhard Muskens
University of Amsterdam
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
Keywords hyperintensionality  higher-order logic  simple theory of types
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DOI 10.2178/jsl/1174668386
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References found in this work BETA

General Semantics.David K. Lewis - 1970 - Synthese 22 (1-2):18--67.
The Proper Treatment of Quantification in Ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.
Ueber Sinn Und Bedeutung (Summary).Gottlob Frege - 1892 - Philosophical Review 1 (5):574-575.
Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.

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Citations of this work BETA

To Be F Is To Be G.Cian Dorr - 2016 - Philosophical Perspectives 30 (1):39-134.
Classicism.Andrew Bacon & Cian Dorr - forthcoming - In Peter Fritz & Nicholas K. Jones (eds.), Higher-order Metaphysics. Oxford University Press.
Closed Structure.Peter Fritz, Harvey Lederman & Gabriel Uzquiano - 2021 - Journal of Philosophical Logic 50 (6):1249-1291.
A Theory of Necessities.Andrew Bacon & Jin Zeng - 2022 - Journal of Philosophical Logic 51 (1):151-199.

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