Transfinite Constructions in Classical Type Theory

2015 ◽  
pp. 391-404 ◽  
Author(s):  
Gert Smolka ◽  
Steven Schäfer ◽  
Christian Doczkal
Keyword(s):  
Type Theory ◽  
Classical Type

scholarly journals Intensional models for the theory of types

2007 ◽  
Vol 72 (1) ◽  
pp. 98-118 ◽  
Author(s):  
Reinhard Muskens
Keyword(s):  
Type Theory ◽  
Possible Worlds ◽  
Sequent Calculus ◽  
Propositional Attitude ◽  
Essential Elements ◽  
Classical Type ◽  
Logical Omniscience ◽  
Small Fragment ◽  
Model Existence ◽  
Model Existence Theorem

AbstractIn 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.

Classical Type Theory

2001 ◽  
pp. 965-1007 ◽  
Author(s):  
Peter B. Andrews
Keyword(s):  
Type Theory ◽  
Classical Type

scholarly journals TPS: A theorem-proving system for classical type theory

1996 ◽  
Vol 16 (3) ◽  
pp. 321-353 ◽  
Author(s):  
Peter B. Andrews ◽  
Matthew Bishop ◽  
Sunil Issar ◽  
Dan Nesmith ◽  
Frank Pfenning ◽  
...  
Keyword(s):  
Theorem Proving ◽  
Type Theory ◽  
Classical Type
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