Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices

被引：5

作者：

Lahav, Ori ^{[1
]}

Zohar, Yoni ^{[2
]}

机构：

[1] Tel Aviv Univ, Tel Aviv, Israel

[2] Bar Ilan Univ, Ramat Gan, Israel

来源：

AUTOMATED REASONING, IJCAR 2022 | 2022年 / 13385卷

关键词：

S4;

D O I：

10.1007/978-3-031-10769-6_28

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A four-valued semantics for the modal logic K is introduced. Possible worlds are replaced by a hierarchy of four-valued valuations, where the valuations of the first level correspond to valuations that are legal w.r.t. a basic non-deterministic matrix, and each level further restricts its set of valuations. The semantics is proven to be effective, and to precisely capture derivations in a sequent calculus for K of a certain form. Similar results are then obtained for the modal logic KT, by simply deleting one of the truth values.

引用

页码：468 / 485

页数：18

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