Open AccessPossibility Semantics for Intuitionistic Logic
Author(s) -
M. J. Cresswell
Publication year - 2004
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v2i0.1764
Subject(s) - intermediate logic , predicate logic , predicate variable , predicate (mathematical logic) , intuitionistic logic , truth value , possible world , classical logic , first order logic , mathematics , propositional calculus , higher order logic , predicate functor logic , many valued logic , closure (psychology) , autoepistemic logic , truth function , set (abstract data type) , computer science , zeroth order logic , description logic , discrete mathematics , theoretical computer science , multimodal logic , programming language , epistemology , philosophy , economics , market economy
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.