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On the extension of intuitionistic propositional logic with Kreisel-Putnam's and Scott's schemes

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Abstract

LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = ((ℸ ℸα→α)→α∨ ℸα)→ ℸα∨ ℸℸα (Scott), andKP = (ℸα→β∨γ)→(ℸα→β)∨(ℸα→γ) (Kreisel-Putnam). Using Kripke's semantics, we prove:

  1. 1)

    SKP has the finite model property;

  2. 2)

    SKP has the disjunction property.

In the last section of the paper we give some results about Scott's logic S = I+S.

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Authors and Affiliations

  1. Department of Philosophy, University of Florence, Florence, Italy

    Pierluigi Minari

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  1. Pierluigi Minari
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Minari, P. On the extension of intuitionistic propositional logic with Kreisel-Putnam's and Scott's schemes. Stud Logica 45, 55–68 (1986). https://doi.org/10.1007/BF01881549

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  • DOI: https://doi.org/10.1007/BF01881549

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