Interpolation and amalgamation; pushing the limits. Part I

Studia Logica 61 (3):311-345 (1998)
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Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open.



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References found in this work

Model-Theoretic Logics.Jon Barwise & Solomon Feferman - 2017 - Cambridge University Press.
Cylindric Algebras.Leon Henkin & Alfred Tarski - 1967 - Journal of Symbolic Logic 32 (3):415-416.
Boolean Algebras with Operators.Alfred Tarski - 1953 - Journal of Symbolic Logic 18 (1):70-71.
What is a logical system?Dov M. Gabbay (ed.) - 1994 - New York: Oxford University Press.

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