scholarly journals On modal components of the S4-logics

10.29007/87kz ◽  
2018 ◽  
Author(s):  
Alexei Y Muravitsky
Keyword(s):  
Modal Logic ◽  
Intermediate Logic ◽  
Grzegorczyk Logic ◽  
Modal Logic S4

We consider the representation of each extension of the modal logic S4 as sum of two components. The first component in such a representation is always included in Grzegorczyk logic and hence contains "modal resources" of the logic in question, while the second one uses essentially the resources of a corresponding intermediate logic. We prove some results towards the conjecture that every S4-logic has a representation with the least component of the first kind.

FORMULAS IN MODAL LOGIC S4

2010 ◽  
Vol 3 (4) ◽  
pp. 600-627
Author(s):  
KATSUMI SASAKI
Keyword(s):  
Normal Form ◽  
Modal Logic ◽  
Propositional Logic ◽  
Normal Forms ◽  
Classical Propositional Logic ◽  
Mutual Relation ◽  
Grzegorczyk Logic ◽  
Modal Logic S4 ◽  
Normal Modal Logics ◽  
Finite Method

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.

QUANTIFIED MODAL LOGIC ON THE RATIONAL LINE

2014 ◽  
Vol 7 (3) ◽  
pp. 439-454 ◽  
Author(s):  
PHILIP KREMER
Keyword(s):  
Modal Logic ◽  
Real Line ◽  
Topological Spaces ◽  
Topological Semantics ◽  
Cantor Space ◽  
Quantified Modal Logic ◽  
Propositional Modal Logic ◽  
The Family ◽  
Modal Logic S4 ◽  
Rational Line

AbstractIn the topological semantics for propositional modal logic, S4 is known to be complete for the class of all topological spaces, for the rational line, for Cantor space, and for the real line. In the topological semantics for quantified modal logic, QS4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. The main result of the current paper is that QS4 is complete, indeed strongly complete, for the rational line.

scholarly journals Modal Logic - a Tool for Design Process Formalisation

10.14311/464 ◽  
2003 ◽  
Vol 43 (5) ◽  
Author(s):  
I. Jelínek
Keyword(s):  
Modal Logic ◽  
Design Process ◽  
Design Knowledge ◽  
The Individual ◽  
Modal Logic S4

In this paper we show the possibility to formalize the design process by means of one type of non-standard logic - modal logic [1]. The type chosen for this study is modal logic S4. The reason for this choice is the ability of this formalism to describe modeling of the individual discrete steps of design, respecting necessity or possibility types of design knowledge.

scholarly journals A New Method to Obtain Termination in Backward Proof Search for Modal Logic S4

2010 ◽  
Vol 20 (1) ◽  
pp. 381-387 ◽  
Author(s):  
R. Pliuskevicius ◽  
A. Pliuskeviciene
Keyword(s):  
Modal Logic ◽  
New Method ◽  
Proof Search ◽  
Modal Logic S4

scholarly journals COMPLETENESS OF SECOND-ORDER PROPOSITIONAL S4 AND H IN TOPOLOGICAL SEMANTICS

2018 ◽  
Vol 11 (3) ◽  
pp. 507-518
Author(s):  
PHILIP KREMER
Keyword(s):  
Modal Logic ◽  
Intuitionistic Logic ◽  
Second Order ◽  
Topological Semantics ◽  
First Order ◽  
Propositional Modal Logic ◽  
Propositional Quantifiers ◽  
Modal Logic S4 ◽  
Natural Way

AbstractWe add propositional quantifiers to the propositional modal logic S4 and to the propositional intuitionistic logic H, introducing axiom schemes that are the natural analogs to axiom schemes typically used for first-order quantifiers in classical and intuitionistic logic. We show that the resulting logics are sound and complete for a topological semantics extending, in a natural way, the topological semantics for S4 and for H.

Complexity of interpolation and related problems in positive calculi

2002 ◽  
Vol 67 (1) ◽  
pp. 397-408 ◽  
Author(s):  
Larisa Maksimova
Keyword(s):  
Modal Logic ◽  
Heyting Algebras ◽  
Logical System ◽  
Complexity Bounds ◽  
Np Completeness ◽  
Interpolation Problems ◽  
Finite Set ◽  
Modal Logic S4 ◽  
Closure Algebras ◽  
Logical Calculi

AbstractWe consider the problem of recognizing important properties of logical calculi and find complexity bounds for some decidable properties. For a given logical system L, a property P of logical calculi is called decidable over L if there is an algorithm which for any finite set Ax of new axiom schemes decides whether the calculus L + Ax has the property P or not. In [11] the complexity of tabularity, pre-tabularity. and interpolation problems over the intuitionistic logic Int and over modal logic S4 was studied, also we found the complexity of amalgamation problems in varieties of Heyting algebras and closure algebras.In the present paper we deal with positive calculi. We prove NP-completeness of tabularity, DP-hardness of pretabularity and PSPACE-completeness of interpolation problem over Int+. In addition to above-mentioned properties, we consider Beth's definability properties. Also we improve some complexity bounds for properties of superintuitionistic calculi.

Loop-free calculus for modal logic S4. I

2012 ◽  
Vol 52 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Julius Andrikonis
Keyword(s):  
Modal Logic ◽  
Modal Logic S4

Loop-free calculus for modal logic S4. II

2012 ◽  
Vol 52 (2) ◽  
pp. 123-133
Author(s):  
Julius Andrikonis
Keyword(s):  
Modal Logic ◽  
Modal Logic S4
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