David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 72 (1):98-118 (2007)
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||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Stefan Hetzl, Alexander Leitsch & Daniel Weller (2011). CERES in Higher-Order Logic. Annals of Pure and Applied Logic 162 (12):1001-1034.
Similar books and articles
Chris Fox & Shalom Lappin, Doing Natural Language Semantics in an Expressive First-Order Logic with Flexible Typing.
Imre Ruzsa (1981). An Approach to Intensional Logic. Studia Logica 40 (3):269 - 287.
Daniel Gallin (1975). Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics. American Elsevier Pub. Co..
J. M. Saul (2002). Intensionality. Aristotelian Society Supplementary Volume 76:75 - 119.
Edward N. Zalta (1988). A Comparison of Two Intensional Logics. Linguistics and Philosophy 11 (1):59-89.
E. H. Alves & J. A. D. Guerzoni (1990). Extending Montague's System: A Three Valued Intensional Logic. Studia Logica 49 (1):127 - 132.
Chris Fox & Shalom Lappin (2004). An Expressive First-Order Logic with Flexible Typing for Natural Language Semantics. Logic Journal of the Interest Group in Pure and Applied Logics 12 (2):135--168.
Matt Fairtlough & Michael Mendler (2003). Intensional Completeness in an Extension of Gödel/Dummett Logic. Studia Logica 73 (1):51 - 80.
Added to index2009-01-28
Total downloads24 ( #76,896 of 1,102,037 )
Recent downloads (6 months)2 ( #192,049 of 1,102,037 )
How can I increase my downloads?