Intensional models for the theory of types

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

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

Similar books and articles

Analytics

Added to PP
2009-01-28

Downloads
195 (#66,178)

6 months
54 (#24,124)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Reinhard Muskens
University of Amsterdam

Citations of this work

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.
A Theory of Necessities.Andrew Bacon & Jin Zeng - 2022 - Journal of Philosophical Logic 51 (1):151-199.
Closed Structure.Peter Fritz, Harvey Lederman & Gabriel Uzquiano - 2021 - Journal of Philosophical Logic 50 (6):1249-1291.

View all 15 citations / Add more citations

References found in this work

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.

View all 18 references / Add more references