Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics
type: Item
instance of: scholarly article
title: Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics
zbMATH Open document ID: 0723.03008
DOI: 10.1007/BF00370365
author: Nobu-Yuki Suzuki
published in: Studia Logica
publication date: 1990-01-01T00:00:00Z
review text: The paper proves some translation theorems for intuitionistic modal logics (IML) using Kripke bundle semantics for intermediate predicate logics (IPL). They are based on the correspondence between Kripke bundles (introduced by the reviewer and \textit{D. P. Skvortsov} [``Semantics of non-classical first-order predicate logics'', in: Mathematical logic (\textit{P. Petkov} (ed.)) (1990)]) and intuitionistic modal frames (introduced by \textit{H. Ono} [Publ. Res. Inst. Math. Sci., Kyoto Univ. 13, 687-722 (1977; Zbl 0373.02026)]). More precisely, let \(\psi\) be a translation from (intuitionistic) modal propositional formulas to predicate formulas transforming \(\square\) to \(\forall x\) and \(\diamondsuit\) to \(\exists x\). An IML K is a modal analogue of an IPL L \((<K,L>\) is an associate, in terms of the paper) iff \(K\vdash A\Leftrightarrow L\vdash \psi (A)\) for any formula A. R. Bull and H. Ono constructed modal analogues of H (intuitionistic logic) and \(H+D\) (the logic of constant domains). The author gives simpler proofs of these results and also finds modal analogues of \(H+\tilde P_ n\), \(H+\tilde P_ n+D\) (\(\tilde P_ n\) is a predicate formula axiomatizing Kripke frames of height \(\leq n)\).
Mathematics Subject Classification ID: 03B55
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03C90
zbMATH DE Number: 4191597
zbMATH Keywords: intuitionistic modal logics
zbMATH Keywords: Kripke bundle semantics
zbMATH Keywords: intermediate predicate logics
zbMATH Keywords: intuitionistic modal frames
MaRDI profile type: Publication
cites work: MIPC as the formalisation of an intuitionist concept of modality
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description: scientific article; zbMATH DE number 4191597