Abstract
The chapter discusses a semantical analysis of intuitionistic logic I. The chapter presents a semantical model theory for Heyting's intuitionist predicate logic and proves the completeness of that system relative to the modeling. The semantics for modal logic that is announced and developed together with the known mappings of intuitionistic logic into the modal system, S4, inspired the present semantics for intuitionist logic. It is important to develop the semantics of intuitionistic logic independently of that of S4; this procedure helps to obtain somewhat more information about intuitionistic logic, including the mapping into S4 as a consequence thereof. In addition to giving a simple decision procedure for Heyting's propositional calculus, the chapter presents the undecidability of monadic intuitionistic quantification theory. The proof is based on the semantics previously developed. Beth semantic tableaux for intuitionistic logic is developed in the chapter. The chapter describes consistency property: in a standard formalization of Heyting's predicate calculus, the axioms are all valid, and the rules preserve validity.
Published Version
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