On Kripke completeness of modal predicate logics around quantified K5

被引：3
|
作者：
Shehtman, Valentin [1 ,2 ]
机构：
[1] Kharkevich Inst Informat Transmiss Problems, B Karetny 19, Moscow 127051, Russia
[2] Natl Res Univ Higher Sch Econ, Moscow, Russia
来源：
ANNALS OF PURE AND APPLIED LOGIC | 2023年 / 174卷 / 02期
关键词：
Modal predicate logic; Kripke completeness; Kripke sheaf; Kripke bundle; Canonical model;
D O I：
10.1016/j.apal.2022.103202
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper studies completeness and incompleteness of modal predicate logics in Kripke semantics, especially for logics of the form QA, minimal predicate extensions of modal propositional logics. We show that QA is incomplete for a continual family of logics A above K + ?(?p -> p), in particular for well-known K5 and K45. On the other hand, in some cases we find completions of QA; 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.( C) 2022 Elsevier B.V. All rights reserved.
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