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Interpolation in fragments of intuitionistic propositional logic

Gerard R. Renardel de Lavalette

Journal of Symbolic Logic 54 (4):1419-1430 (1989)

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The Beth Property in Algebraic Logic.W. J. Blok & Eva Hoogland - 2006 - Studia Logica 83 (1-3):49-90.details The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics. Download Export citation Bookmark 12 citations
Doing logic by computer: interpolation in fragments of intuitionistic propositional logic.Lex Hendriks - 2000 - Annals of Pure and Applied Logic 104 (1-3):97-112.details In this paper we study the interpolation property in fragments of intuitionistic and propositional logic, using both proof theoretic and semantic techniques. We will also sketch some computational methods, based on the semantical techniques introduced, to obtain counterexamples in fragment where interpolation does not hold. Download Export citation Bookmark 1 citation
(1 other version)Interpolation in fragments of intuitionistic propositional logic.Gerard R. Renardel de Lavalette - 1989 - Journal of Symbolic Logic 54 (4):1419-1430.details We show in this paper that all fragments of intuitionistic propostional logic based on a subset of the connectives $\wedge, \vee, \rightarrow, \neg$ satisfy interpolation. Fragments containing $\leftrightarrow$ or $\neg\neg$ are briefly considered. Download Export citation Bookmark 4 citations

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