An almost general splitting theorem for modal logic. (English) Zbl 0732.03012
The idea of a splitting in modal logic is this: given a logic L, is there a logic L/A \((=\) the splitting of L by the algebraic model A) whose models are all the L-models that omit A \((=\) the variety they generate does not contain A).
The purpose of this paper is to present an “almost” general characterization of all algebras which split L for an arbitrary normal modal logic without any assumptions of transitivity. The author allows the language to have more than one modal operator, and also the splitting algebra to be infinite.
The purpose of this paper is to present an “almost” general characterization of all algebras which split L for an arbitrary normal modal logic without any assumptions of transitivity. The author allows the language to have more than one modal operator, and also the splitting algebra to be infinite.
Reviewer: L.Esakia (Tbilisi)
MSC:
| 03B45 | Modal logic (including the logic of norms) |
| 03G25 | Other algebras related to logic |
| 06E25 | Boolean algebras with additional operations (diagonalizable algebras, etc.) |
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