On Kripke completeness of modal predicate logics around quantified K5статья
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Дата последнего поиска статьи во внешних источниках: 17 июля 2024 г.
Аннотация:The paper studies completeness and incompleteness of modal predicate logics in
Kripke semantics, especially for logics of the form QL, minimal predicate extensions
of modal propositional logics. We show that QL is incomplete for a continual family
of logics, in particular for well-known K5 and K45. On the other hand, in some cases we find completions of QL; they are obtained by
adding a single extra axiom. Completeness proofs use canonical models, with some
modifications, and the case of QK5 is the most interesting from the technical side.
We also introduce the “boxing” operation for modal predicate logics and prove
transfer results for Kripke and Kripke sheaf completeness with respect to this
operation.