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

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.

scholarly journals Subformula Linking for Intuitionistic Logic with Application to Type Theory

2021 ◽  
pp. 200-216
Author(s):  
Kaustuv Chaudhuri
Keyword(s):  
Theorem Proving ◽  
Intuitionistic Logic ◽  
Type Theory ◽  
Linear Logic ◽  
Interactive Theorem Proving ◽  
Order Logic ◽  
First Order Logic ◽  
Direct Manipulation ◽  
First Order

AbstractSubformula linking is an interactive theorem proving technique that was initially proposed for (classical) linear logic. It is based on truth and context preserving rewrites of a conjecture that are triggered by a user indicating links between subformulas, which can be done by direct manipulation, without the need of tactics or proof languages. The system guarantees that a true conjecture can always be rewritten to a known, usually trivial, theorem. In this work, we extend subformula linking to intuitionistic first-order logic with simply typed lambda-terms as the term language of this logic. We then use a well known embedding of intuitionistic type theory into this logic to demonstrate one way to extend linking to type theory.

Transfinite Constructions in Classical Type Theory

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

System Description: TPS: A Theorem Proving System for Type Theory

2000 ◽  
pp. 164-169 ◽  
Author(s):  
Peter B. Andrews ◽  
Matthew Bishop ◽  
Chad E. Brown
Keyword(s):  
Theorem Proving ◽  
Type Theory ◽  
System Description
Sign in / Sign up

Export Citation Format

Share Document