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FORMULAS IN MODAL LOGIC S4

Published online by Cambridge University Press:  13 September 2010

KATSUMI SASAKI
KATSUMI SASAKI*
Affiliation:
Nanzan University
*
*FACULTY OF INFORMATION SCIENCES AND ENGINEERING, NANZAN UNIVERSITY, 27 SEIREI-CHO, SETO 489-0863, JAPAN. E-mail:sasaki@nanzan-u.ac.jp
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Abstract

Here, we provide a detailed description of the mutual relation of formulas with finite propositional variables p1, …, pm in modal logic S4. Our description contains more information on S4 than those given in Shehtman (1978) and Moss (2007); however, Shehtman (1978) also treated Grzegorczyk logic and Moss (2007) treated many other normal modal logics. Specifically, we construct normal forms, which behave like the principal conjunctive normal forms in the classical propositional logic. The results include finite and effective methods to find a normal form equivalent to a given formula A by clarifying the behavior of connectives and giving a finite method to list all exact models.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 4 , December 2010 , pp. 600 - 627
Copyright
Copyright © Association for Symbolic Logic 2010

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