Interpolation in algebraizable logics semantics for non-normal multi-modal logic. (English) Zbl 0918.03014
The paper is rich in new results and ideas which are impossible to render adequately here. Therefore we shall limit ourselves to indicate the nature of the results. The author extends Maksimova’s Theorem (that a normal modal logic has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property) to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics. The author also develops a more general possible worlds semantics for not necessarily normal multi-modal logics with arbitrarily many modalities.
Reviewer: L.Esakia (Tbilisi)
MSC:
| 03B45 | Modal logic (including the logic of norms) |
| 03G25 | Other algebras related to logic |
| 03C40 | Interpolation, preservation, definability |
| 06E25 | Boolean algebras with additional operations (diagonalizable algebras, etc.) |
Keywords:
Craig interpolation; amalgamation; multi-modal logic; Boolean algebra with operators; possible worlds semanticsReferences:
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