The Completeness Problem for Modal Logic

被引：2
|
作者：
Achilleos, Antonis [1 ]
机构：
[1] Reykjavik Univ, Sch Comp Sci, Reykjavik, Iceland
来源：
LOGICAL FOUNDATIONS OF COMPUTER SCIENCE (LFCS 2018) | 2018年 / 10703卷
关键词：
Modal logic; Completeness; Computational complexity; Bisimulation; COMPLEXITY; FORMULAS;
D O I：
10.1007/978-3-319-72056-2_1
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic. We discover that completeness and validity have the same complexity - with certain exceptions for which there are, in general, no complete formulas. To prove upper bounds, we present a non-deterministic polynomial-time procedure with an oracle from PSPACE that combines tableaux and a test for bisimulation, and determines whether a formula is complete.
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页码：1 / 21
页数：21
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