Possibility Semantics for Intuitionistic Logic

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

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.

Author Biography

M. J. Cresswell, Department of Philosophy, University of Auckland. Department of Philosophy, Texas A&M University
Published
2004-04-30
How to Cite
CRESSWELL, M. J.. Possibility Semantics for Intuitionistic Logic. The Australasian Journal of Logic, [S.l.], v. 2, apr. 2004. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1764>. Date accessed: 18 july 2019. doi: https://doi.org/10.26686/ajl.v2i0.1764.