A Sufficient Condition for the Finite Model Property of Modal Logics above K4

1993 ◽  
Vol 1 (1) ◽  
pp. 13-21 ◽  
Author(s):  
MICHAEL ZAKHARYASCHEV
Keyword(s):  
Modal Logics ◽  
Finite Model ◽  
Sufficient Condition ◽  
Model Property ◽  
Finite Model Property

Decidability of interpretability logics ILM0 and ILW*

2017 ◽  
Vol 25 (5) ◽  
pp. 758-772 ◽  
Author(s):  
Luka Mikec ◽  
Tin Perkov ◽  
Mladen Vuković
Keyword(s):  
Open Problem ◽  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Filtration Method ◽  
Finite Model Property ◽  
Missing Link ◽  
Interpretability Logic

Abstract The finite model property is a key step in proving decidability of modal logics. By adapting the filtration method to the generalized Veltman semantics for interpretability logics, we have been able to prove the finite model property of interpretability logic ILM0 w.r.t. generalized Veltman models. We use the same technique to prove the finite model property of interpretability logic ILW* w.r.t. generalized Veltman models. The missing link needed to prove the decidability of ILM0 was completeness w.r.t. generalized Veltman models, which we obtain in this article. Thus, we prove the decidability of ILM0, which was an open problem. Using the same technique, we prove that ILW* is also decidable.

Simulating polyadic modal logics by monadic ones

2003 ◽  
Vol 68 (2) ◽  
pp. 419-462 ◽  
Author(s):  
George Goguadze ◽  
Carla Piazza ◽  
Yde Venema
Keyword(s):  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
First Order ◽  
First Order Definability

AbstractWe define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λsim in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability.

scholarly journals A Finite Model Property for Gödel Modal Logics

2013 ◽  
pp. 226-237 ◽  
Author(s):  
Xavier Caicedo ◽  
George Metcalfe ◽  
Ricardo Rodríguez ◽  
Jonas Rogger
Keyword(s):  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property

The finite model property in tense logic

1995 ◽  
Vol 60 (3) ◽  
pp. 757-774 ◽  
Author(s):  
Frank Wolter
Keyword(s):  
Modal Logics ◽  
Tense Logic ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Negative Results ◽  
Propositional Language ◽  
Positive Results

AbstractTense logics in the bimodal propositional language are investigated with respect to the Finite Model Property. In order to prove positive results techniques from investigations of modal logics above K4 are extended to tense logic. General negative results show the limits of the transfer.

scholarly journals New New Modification of the Subformula Property for a Modal Logic

2020 ◽  
Author(s):  
Mitio Takano
Keyword(s):  
Modal Logic ◽  
Natural Extension ◽  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Additional Axiom ◽  
Subformula Property

A modified subformula property for the modal logic KD with the additional axiom $\Box\Diamond(A\vee B)\supset\Box\Diamond A\vee\Box\Diamond B$ is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown (Bull Sect Logic 30:115--122, 2001 and 48:19--28, 2019). The finite model property as well as decidability for the logic follows from this.

Canonical formulas for K4. Part III: the finite model property

1997 ◽  
Vol 62 (3) ◽  
pp. 950-975 ◽  
Author(s):  
Michael Zakharyaschev
Keyword(s):  
Sufficient Conditions ◽  
Modal Logics ◽  
Point Of View ◽  
Normal Extension ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Modal Reduction ◽  
Canonical Formulas ◽  
General Frames

This paper, a continuation of the series [22, 24], presents two methods for establishing the finite model property (FMP, for short) of normal modal logics containing K4. The methods are oriented mainly to logics represented by their canonical axioms and yield for such axiomatizations several sufficient conditions of FMP. We use them to obtain solutions to two well known open FMP problems. Namely, we prove that• every normal extension of K4 with modal reduction principles has FMP and• every normal extension of S4 with a formula of one variable has FMP.These results are interesting not only from the technical point of view. Actually, they reveal important properties of a quite natural family of modal logics—formulas of one variable and, in particular, modal reduction principles are typical axioms in modal logic. Unfortunately, the technical apparatus developed in this paper is applicable only to logics with transitive frames, and the situation with FMP of extensions of K by modal reduction principles, even by axioms of the form □np → □mp still remains unclear. I think at present this is one of the major challenges in completeness theory.The language of the canonical formulas, introduced in [22] (I'll refer to that paper as Part I), is a way of describing the “geometry and topology” of formulas' refutation (general) frames by means of some finite refutation patterns.

Finite model property of modal logics of finite depth

2016 ◽  
Vol 71 (1) ◽  
pp. 164-166
Author(s):  
A V Kudinov ◽  
I B Shapirovsky
Keyword(s):  
Finite Depth ◽  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property

scholarly journals A Finite Model Property for Gödel Modal Logics

10.29007/vgh2 ◽  
2018 ◽  
Author(s):  
Xavier Caicedo ◽  
George Metcalfe ◽  
Ricardo Rodriguez ◽  
Jonas Rogger
Keyword(s):  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
First Order ◽  
Gödel Logic ◽  
Np Completeness ◽  
Kripke Frames ◽  
The One

A new semantics with the finite model property is provided and used to establish decidability for Gödel modal logics based on (crisp or fuzzy) Kripke frames combined locally with Gödel logic. A similar methodology is also used to establish decidability, indeed co-NP-completeness, for a Gödel S5 logic that coincides with the one-variable fragment of first-order Gödel logic.

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