Possibility Semantics for Intuitionistic Logic

Authors

  • M. J. Cresswell Department of Philosophy, University of Auckland. Department of Philosophy, Texas A&M University

DOI:

https://doi.org/10.26686/ajl.v2i0.1764

Abstract

The paper investigates interpretations of propositional and first-order logic in which validity is defined in terms of partial indices; sometimes called possibilities but here understood as non-empty subsets of a set W of possible worlds. Truth at a set of worlds is understood to be truth at every world in the set. If all subsets of W are permitted the logic so determined is classical first-order predicate logic. Restricting allowable subsets and then imposing certain closure conditions provides a modelling for intuitionistic predicate logic. The same semantic interpretation rules are used in both logics for all the operators.

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Author Biography

M. J. Cresswell, Department of Philosophy, University of Auckland. Department of Philosophy, Texas A&M University

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Published

2004-04-30