Craig's interpolation theorem for the intuitionistic logic and its extensions - a semantical approach
type: Item
instance of: scholarly article
title: Craig's interpolation theorem for the intuitionistic logic and its extensions - a semantical approach
zbMATH Open document ID: 0617.03008
DOI: 10.1007/BF01881546
author: Hiroakira Ono
published in: Studia Logica
publication date: 1986-01-01T00:00:00Z
review text: Craig's interpolation theorem for intuitionistic predicate logic was first proved by Schütte using syntactical methods. Other syntactical proofs were given by, among others, Prawitz and Maehara. Semantical proofs were given by Gabbay, Fitting and Ono. One more such proof is given here, along the lines of the Henkin-style proof of the completeness theorem. Using a generalized notion of inseparable pair of theories, the author clarifies the relationship between interpolation and (Robinson's) consistency. As a corollary, the author also gives a new proof of the interpolation property of the seven intermediate propositional logics listed in \textit{L. L. Maksimova}'s paper in Algebra Logika 16, 643-681 (1977; Zbl 0403.03047). Warning: in reference [14], H. Ono should be replaced by K. \((=\) Katuzi) Ono, H. Ono's father.
reviewed by: Daniele Mundici
Mathematics Subject Classification ID: 03B55
Mathematics Subject Classification ID: 03C40
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03F05
zbMATH DE Number: 3999889
zbMATH Keywords: semantical proof
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: intermediate logic
zbMATH Keywords: joint consistency
zbMATH Keywords: inseparable theories
zbMATH Keywords: Robinson's theorem
zbMATH Keywords: Craig's interpolation
zbMATH Keywords: intuitionistic predicate logic
zbMATH Keywords: inseparable pair of theories
zbMATH Keywords: intermediate propositional logics
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01881546
OpenAlex ID: W2000897924
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description: scientific article; zbMATH DE number 3999889