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In this paper we introduce the modelwise interpolation property of a logic that states that whenever \(\models\phi\to\psi\) holds for two formulas \(\phi\) and \(\psi\), then for every model \(\mathfrak{M}\) there is an interpolant formula \(\chi\) formulated in the intersection of the vocabularies of \(\phi\) and \(\psi\), such that \(\mathfrak{M}\models\phi\to\chi\) and \(\mathfrak{M}\models\chi\to\psi\), that is, the interpolant formula in Craig interpolation may vary from model to model. We compare the modelwise interpolation property with the standard Craig interpolation and with the local interpolation property by discussing examples, most notably the finite variable fragments of first order logic, and difference logic. As an application we connect the modelwise interpolation property with the local Beth definability, and we prove that the modelwise interpolation property of an algebraizable logic can be characterized by a weak form of the superamalgamation property of the class of algebras corresponding to the models of the logic.

In this paper we introduce the modelwise interpolation property of a logic that states that whenever |= ϕ → ψ holds for two formulas ϕ and ψ, then for every model M there is an interpolant formula χ formulated in the intersection of the vocabularies of ϕ and ψ, such that M |= ϕ → χ and M |= χ → ψ, that is, the interpolant formula in Craig interpolation may vary from model to model. We compare the modelwise interpolation property with the standard Craig interpolation and with the local interpolation property by discussing examples, most notably the finite variable fragments of first order logic, and difference logic. As an application we connect the modelwise interpolation property with the local Beth definability, and we prove that the modelwise interpolation property of an algebraizable logic can be characterized by a weak form of the superamalgamation property of the class of algebras corresponding to the models of the logic. [ABSTRACT FROM AUTHOR]

We prove that there is infinitely many tabular modal logics extending KB:Alt(2) which have interpolation. [ABSTRACT FROM AUTHOR]

The sole purpose of this paper is to give an algebraic characterization, in terms of a superamalgamation property, of a local version of Craig interpolation theorem that has been introduced and studied in earlier papers. We continue ongoing research in abstract algebraic logic and use the framework developed by Andréka{ Németi and Sain. [ABSTRACT FROM AUTHOR]

The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic. [ABSTRACT FROM AUTHOR]