Denotations for classical proofs - Preliminary results (1992)
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BibTeX
@MISC{Groote92denotationsfor,
author = {Philippe de Groote},
title = {Denotations for classical proofs - Preliminary results},
year = {1992}
}
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Abstract
This paper addresses the problem of extending the formulae-as-types principle to classical logic. More precisely, we introduce a typed lambda-calculus (-LK ! ) whose inhabited types are exactly the implicative tautologies of classical logic and whose type assignment system is a classical sequent calculus. Intuitively, the terms of -LK ! correspond to constructs that are highly non-deterministic. This intuition is made much more precise by providing a simple model where the terms of -LK ! are interpreted as non-empty sets of (interpretations of) untyped lambda-terms. We also consider the system (-LK ! + cut) and investigate the relation existing between cut elimination and reduction. Finally, we show how to extend our system in order to take conjunction, disjunction and negation into account. 1 Introduction In: Logical Foundations of Computer Science Tver'92, A. Nerode, M. Taitslin (Eds.), Lecture Notes in Computer Science, Vol. 620, Springer-Verlag (1992), pp. 105-116. In thi...
