Some results on the Kripke sheaf semantics for super-intuitionistic predicate logics
type: Item
instance of: scholarly article
title: Some results on the Kripke sheaf semantics for super-intuitionistic predicate logics
zbMATH Open document ID: 0772.03009
DOI: 10.1007/BF01053065
author: Nobu-Yuki Suzuki
published in: Studia Logica
publication date: 1993-05-16T00:00:00Z
review text: ``Kripke sheaf semantics'' (which is equivalent to the semantics of predicate Kripke frames with equality) was introduced by the reviewer and \textit{D. Skvortsov} [``Semantics of nonclassical first-order predicate logics'', Mathematical logic, Proc. Summer Sch. Conf. Ded. 90th Anniv. Arend Heyting, Chaika/Bulg. 1988, 105-116 (1990)]. As was stated there, Kripke sheaf semantics is richer than standard Kripke semantics already for logics without equality. The present paper proves a stronger result; namely, it gives simple examples of finitely axiomatizable superintuitionistic predicate logics without equality, which ae complete in Kripke sheaf semantics but incomplete in standard Kripke semantics. In particular, every logic \(H+J+D+\neg\neg\bigl(\exists x p(x)\supset\forall x p(x)\bigr)\), with \(J\) tabular, has these properties (\(H\) denotes Heyting predicate logic, \(D\) is the axiom of constant domains). The paper also contains a correction of an error in the author's earlier paper [ibid. 49, 289-306 (1990; Zbl 0723.03008)].
Mathematics Subject Classification ID: 03B55
zbMATH DE Number: 165914
zbMATH Keywords: \(p\)-morphism
zbMATH Keywords: Kripke bundle
zbMATH Keywords: algebraic semantics
zbMATH Keywords: Kripke sheaf semantics
zbMATH Keywords: superintuitionistic predicate logics without equality
reviewed by: Valentin Shehtman
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01053065
OpenAlex ID: W2058351460
description: scientific article; zbMATH DE number 165914