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STABLE MODAL LOGICS

GURAM BEZHANISHVILI, NICK BEZHANISHVILI, JULIA ILIN
2018 The Review of Symbolic Logic  
AbstractStable logics are modal logics characterized by a class of frames closed under relation preserving images. These logics admit all filtrations.  ...  Since many basic modal systems such as K4 and S4 are not stable, we introduce the more general concept of an M-stable logic, where M is an arbitrary normal modal logic that admits some filtration.  ...  Acknowledgements We are very grateful to the referees for many useful suggestions that have substantially improved the paper. We also thank Frederik M. Lauridsen for helpful discussions.  ... 
doi:10.1017/s1755020317000375 fatcat:e4pqhrqwfjei3lgwblw5h4bwdi

Page 5290 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
We establish gen- eral sufficient conditions for the absence of fmp with respect to admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic 4 containing K4 with  ...  This truly constructive method allows the finite model property to be established in many circumstances without consid- ering infinite models.  ... 

Description of modal logics inheriting admissible rules for S4

V. Rybakov
1999 Logic Journal of the IGPL  
We give a necessary and sufficient condition for any modal logic with fmp to inherit all inference rules admissible in S4.  ...  Using this condition we describe all tabular modal logics inheriting inference rules admissible for S4.  ...  Acknowledgements This research was supported by the Russian Science Foundation (RFFI) and by the Turkish Scientific Technical Research Council (TUBITAK, Ankara) during the visit of V.V.Rybakov to the Mathematics  ... 
doi:10.1093/jigpal/7.5.655 fatcat:4fahyok2hraydfyhm653mms2qq

STABLE CANONICAL RULES

GURAM BEZHANISHVILI, NICK BEZHANISHVILI, ROSALIE IEMHOFF
2016 Journal of Symbolic Logic (JSL)  
We also define stable multi-conclusion consequence relations and stable logics and prove that these systems have the finite model property.  ...  We apply these results to construct finite refutation patterns for modal formulas, and prove that each normal modal logic is axiomatizable by stable canonical rules.  ...  The second and third authors acknowledge the support of the Netherlands Organization for Scientific Research under grant 639.032.918.  ... 
doi:10.1017/jsl.2015.54 fatcat:r7blvg4ef5cqlixckwmgfgihte

Willem Blok and Modal Logic

W. Rautenberg, M. Zakharyaschev, F. Wolter
2006 Studia Logica: An International Journal for Symbolic Logic  
Blok's contribution to modal logic. Presented by ; Received Studia Logica 0: 1-??, 2006.  ...  Acknowledgements We are grateful to Alexander Chagrov, Rob Goldblatt, Ian Hodkinson, Johan van Benthem, and the editors of this special issue for their comments and suggestions.  ...  Every modal or si-logic with the finite model property can be represented as an intersection of tabular logics.  ... 
doi:10.1007/s11225-006-8296-2 fatcat:34qovm5c6jd3hb3xqjz5wvvm4u

MacNeille completion and profinite completion can coincide on finitely generated modal algebras

Jacob Vosmaer
2009 Algebra Universalis  
Specific examples of such modal algebras are the free K4-algebra and the free PDL-algebra.  ...  Specifically, we show that if A is a residually finite, finitely generated modal algebra such that HSP(A) has equationally definable principal congruences, then the profinite completion of A is isomorphic  ...  The author would like to thank Yde Venema, who suggested that Theorem 4.2 might be true. Additionally, the author is grateful to the Editor and the Referee for their criticisms and suggestions.  ... 
doi:10.1007/s00012-009-0028-9 fatcat:jf5t22ui7vfrlhrk3q7ljn2yce

Unifiability in extensions of K4

C. Gencer, D. De Jongh
2009 Logic Journal of the IGPL  
We extend and generalize the work on unifiability of [8] . We give a semantic characterization for unifiability and non-unifiability in the extensions of K4.  ...  We apply this in particular to extensions of KD4, GL and K4.3 to obtain a syntactic characterization and give a concrete decision procedure for unifiability for those logics.  ...  We thank TÜBİTAK (The Technical and Research Council of Türkiye) for supporting this work.  ... 
doi:10.1093/jigpal/jzn032 fatcat:o4hsy6cr4jg3zahbps4qw4awmi

Splittings and the finite model property

Marcus Kracht
1993 Journal of Symbolic Logic (JSL)  
AbstractAn old conjecture of modal logics states that every splitting of the major systemsK4, S4, GandGrzhas the finite model property.  ...  The proof works by establishing a rather strong property of these splitting frames namely that they preserve the finite model property in the following sense.  ...  Introduction An old problem of modal logic is to prove that all splittings of K4 or other important systems have the finite model property (fmp).  ... 
doi:10.2307/2275330 fatcat:hyymox4e3nctnipzj3twgxmkde

Canonical rules

Emil Jeřábek
2009 Journal of Symbolic Logic (JSL)  
relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property.  ...  Other applications of canonical rules include a generalization of the Blok–Esakia theorem and the theory of modal companions to systems of multiple-conclusion rules or (unitary structural global) consequence  ...  If L has the finite model property as a logic, then it also has the finite model property as a rule system.Proof: Let L .  ... 
doi:10.2178/jsl/1254748686 fatcat:4mt72ynkybhihaaonpwt5w64xe

Free Modal Algebras Revisited: The Step-by-Step Method [chapter]

Nick Bezhanishvili, Silvio Ghilardi, Mamuka Jibladze
2014 Leo Esakia on Duality in Modal and Intuitionistic Logics  
We review the step-by-step method of constructing finitely generated free modal algebras. First we discuss the global step-by-step method, which works well for rank one modal logics.  ...  In particular, we show that it works well for constructing the finitely generated free algebras for such well-known modal systems as T, K4 and S4.  ...  Acknowledgements The authors are very grateful to the referee for many useful suggestions that improved the presentation of the paper.  ... 
doi:10.1007/978-94-017-8860-1_3 fatcat:g2had7basnd3xj5uu76hhr5fna

A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae [chapter]

Renate A. Schmidt, Ullrich Hustadt
2003 Lecture Notes in Computer Science  
In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity  ...  The goal of the axiomatic translation principle is to find simplified theories, which capture the inference problems in the original theory, but in a way that is more amenable to automation and easier  ...  As for the finite model property, we believe the finite model property of the logics K5 κ and Kalt κ1,κ2 1 has been open up to now.  ... 
doi:10.1007/978-3-540-45085-6_36 fatcat:l4qebca3gba4xpz3exmdfzg3i4

Unification in modal and description logics

F. Baader, S. Ghilardi
2010 Logic Journal of the IGPL  
In this article, we give a survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics.  ...  As mentioned above, the big open problem for unification in modal logics is decidability of unification in the modal logic K.  ...  The logics K ∀ , K4 ∀ , GL ∀ , . . . are the universal modality counterparts of K, K4, . . .  ... 
doi:10.1093/jigpal/jzq008 fatcat:hrew2tewyrfopf2a5egnmhm23q

The bounded proof property via step algebras and step frames

Nick Bezhanishvili, Silvio Ghilardi
2014 Annals of Pure and Applied Logic  
the finite model property.  ...  We define conservative one-step frames and prove that every finite conservative one-step frame for Ax is a p-morphic image of a finite Kripke frame for L iff Ax has the bounded proof property and L has  ...  We show that an axiomatic system Ax axiomatizing a logic L has the bpp and the finite model property (the fmp) iff every one step-frame validating Ax is a p-morphic image of a finite Kripke frame for L  ... 
doi:10.1016/j.apal.2014.07.005 fatcat:xnysswa2n5dyzkrqqg2crn5kbe

Completing the Picture: Complexity of Graded Modal Logics with Converse [article]

Bartosz Bednarczyk, Emanuel Kieroński, Piotr Witkowski
2021 arXiv   pre-print
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established.  ...  By "traditional" classes of frames, we mean those characterized by any positive combination of reflexivity, seriality, symmetry, transitivity, and the Euclidean property.  ...  Acknowledgements We thank Evgeny Zolin for providing us a comprehensive list of gaps in the classification of the complexity of graded modal logics and for sharing with us his tikz files with modal cubes  ... 
arXiv:1812.04413v5 fatcat:wck54wwwdjfxxb7q6wo67ze4bq

Coherence in Modal Logic [article]

Tomasz Kowalski, George Metcalfe
2019 arXiv   pre-print
In this paper, a more general criterion is obtained and used to prove the failure of coherence and uniform deductive interpolation for a broad family of modal logics, including K, KT, K4, and S4.  ...  In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive interpolation property for equational consequence in a variety, and a general criterion was  ...  sufficient condition for the failure of coherence in a modal logic.  ... 
arXiv:1902.02540v1 fatcat:twg72iaqlbbsvlgdeij6eohhby
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