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Denotations for classical proofs -Preliminary results-

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Logical Foundations of Computer Science — Tver '92 (LFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 620))

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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 (λ-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 λ-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 λ-LK→ are interpreted as non-empty sets of (interpretations of) untyped lambda-terms. We also consider the system (λ-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.

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Authors and Affiliations

  1. Unité d'Informatique, Université Catholique de Louvain, BE-1348, Louvain-la-Neuve, Belgium

    Philippe de Groote

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  1. Philippe de Groote
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Editor information

Anil Nerode Mikhail Taitslin

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© 1992 Springer-Verlag Berlin Heidelberg

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de Groote, P. (1992). Denotations for classical proofs -Preliminary results-. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023867

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  • DOI: https://doi.org/10.1007/BFb0023867

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55707-4

  • Online ISBN: 978-3-540-47276-6

  • eBook Packages: Springer Book Archive

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