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## Neighbourhood Frame Product KxK

P. 373-386.

We consider modal logics of products of neighborhood frames and nd the modal logic of all products of normal neighborhood frames.

Language:
English

Shehtman V. B., Russian Mathematical Surveys 2012 Vol. 67 No. 4 P. 721-777

This paper studies two-dimensional modal logics of a special type, 'Segerberg squares'. They are defined as the usual squares of modal logics with additional connectives corresponding to the diagonal symmetry and the two projections onto the diagonal. For these logics a finite axiomatization is constructed in many cases, and completeness and the finite model property ...

Added: February 4, 2013

Kudinov A., , in : Advances in Modal Logic. Issue 9.: L. : College Publications, 2012. P. 286-294.

We consider modal logics of products of neighborhood frames and prove that for any pair L and L' of logics from set {S4, D4, D, T} modal logic of products of L-neighborhood frames and L'-neighborhood frames is the fusion of L and L'. ...

Added: February 21, 2013

Shehtman V. B., , in : Advances in Modal Logic, Volume 10. : College Publications, 2014. P. 498-512.

The paper deals with a special type of filtration in modal logic called "canonical". This filtration has been known since the 1970s, but was used only occasionally. Applying it in a systematic way allows us to prove new results on finite model property (and in some cases --- local tabularity) for different polymodal logics. ...

Added: September 18, 2015

Kudinov A., Shehtman V. B., Shapirovsky I., , in : Advances in Modal Logic. Issue 9.: L. : College Publications, 2012. P. 395-410.

With a set S of words in an alphabet A we associate the frame (S; H), where sHt iff s and t are words of the same length and h(s; t) = 1 for the Hamming distance h. We investigate some unimodal logics of these frames. We show that if the length of words n ...

Added: February 21, 2013

L. : College Publications, 2012

Advances in Modal Logic is a bi-annual international conference and book series in Modal Logic. The aim of the conference series is to report on important new developments in pure and applied modal logic, and to do so at varying locations throughout the world. The book series is based on the conferences. Please consult thebackground pages for further details. ...

Added: February 21, 2013

L. : College Publications, 2016

Logic deals with the fundamental notions of truth and falsity. Modal logic arose from the philosophical study of “modes of truth” with the two most common modes being “necessarily true” and “possibly true”. Research in modal logic now spans the spectrum from philosophy, computer science and mathematics using techniques from relational structures, universal algebra, topology, ...

Added: July 17, 2017

Zolin E., Journal of Logic and Computation 2017 Vol. 27 No. 5 P. 1399-1420

We extend the language of the modal logic K4 of transitive frames with two sorts of modalities. In addition to the usual possibility modality (which means that a formula holds in some successor of a given point), we consider graded modalities (a formula holds in at least n successors) and converse graded modalities (aformula holds ...

Added: June 14, 2018

Rybakov M., Shkatov D., Studia Logica 2024

In the early 1960s, to prove undecidability of monadic fragments of sublogics of the predicate modal logic QS5 that include the classical predicate logic QCl, Saul Kripke showed how a classical atomic formula with a binary predicate letter can be simulated by a monadic modal formula. We consider adaptations of Kripke's simulation, which we call the Kripke trick, to various modal ...

Added: December 2, 2023

Rybakov M., Shkatov D., , in : Десятые Смирновские чтения: материалы Междунар. науч. конф., Москва, 15–17 июня 2017 г. : М. : Современные тетради, 2017. P. 45-45.

We discuss an example of recursively-enumerable Kripke-complete first-order modal logics that are not Kripke complete with respect to a first-order definable class of frames. ...

Added: October 7, 2019

Gabbay D., Shapirovsky I., Shehtman V. B., Journal of Applied Logic 2014 Vol. 12 No. 4 P. 570-583

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. ...

Added: March 24, 2015

Kudinov A., Logic Journal of the IGPL 2018 Vol. 26 No. 3 P. 316-338

The paper considers modal logics of products of neighbourhood frames. The n-product of modal logics is the logic of all products of neighbourhood frames of the corresponding logics. We find the n-product of any two pretransitive Horn axiomatizable logics. As a corollary, we find the d-logic of products of topological spaces from some classes of ...

Added: August 20, 2018

Kikot S., Kudinov A., Mathematics 2022 Vol. 10 No. 19 Article 3701

We axiomatize strictly positive fragments of modal logics with the confluence axiom. We consider unimodal logics such
as K.2, D.2, D4.2 and S4.2
with unimodal confluence $\Diamond\Box p \to \Box\Diamond p$
as well as the products of modal logics
in the set {K, D, T, D4, S4}, which contain bimodal confluence
$\Diamond_1\Box_2 p \to \Box_2\Diamond_1 p$.
We show that the impact ...

Added: October 10, 2022

Khaitovich D., / Cornell University. Series arXiv "math". 2021. No. 2110.

Added: December 7, 2021

Marseille : [б.и.], 2011

Added: February 27, 2013

Kudinov A., Shapirovsky I., , in : Topology, Algebra and Categories in Logic (TACL 2011). : Marseille : [б.и.], 2011. P. 261-264.

We consider propositional normal unimodal pretransitive logics, i.e., logics with expressible `transitive' modality. There is a long-standing open problem about the finite model property (fmp) and decidability of pretransitive logics, in particular - for the logics K^m_n = K+[]^m p -> []^n p, n>m>1. ...

Added: February 27, 2013

Complexity function and complexity of validity of modal and superintuitionistic propositional logics

Rybakov M., Shkatov D., Journal of Logic and Computation 2023 Vol. 33 No. 7 P. 1566-1595

We consider the relationship between the algorithmic properties of the validity problem for a modal or superintuitionistic propositional logic and the size of the smallest Kripke countermodels for non-theorems of the logic. We establish the existence, for every degree of unsolvability, of a propositional logic whose validity problem belongs to the degree and whose every ...

Added: January 6, 2023

Shehtman V. B., Shapirovsky I., , in : Advances in Modal Logic. Vol. 11.: L. : College Publications, 2016. P. 520-534.

According to the classical result by Segerberg and Maksimova, a modal logic containing K4 is locally tabular iff it is of finite height. The notion of finite height can also be defined for logics, in which the master modality is expressible (‘pretransitive’ logics). We observe that any locally tabular logic is pretransitive of finite height. Then we prove some ...

Added: September 20, 2018

Zolin E., Notre Dame Journal of Formal Logic 2019

We introduce a modal operator of weak necessity, inspired by the canonical model construction for the non-contingency logic developed by Humberstone and Kuhn in 1995. This operator, when applied to a proposition, means that all consequences of a given proposition are non-contingent. We show that, although the weak necessity has many properties inherent to normal ...

Added: June 14, 2018

Slavnov S. A., Moscow Mathematical Journal 2005 Vol. 5 No. 2 P. 477-492

Классический результат о топологической семантике модальных логик, принадлежащий МакКинси и Тарскому (и часто называемый теоремой Тарского), состоит в полноте логики S4 по отношению к интерпретациям в пространстве R^n
для любого n. В последнее время разные авторы рассматривали динамические топологические логики, которые интерпретируются в динамических пространствах (абстрактных динамических системах). Динамическое пространство – это топологическое пространство вместе с непрерывной функцией на нем. В работе Артёмова, Даворен и ...

Added: February 27, 2013

Kudinov A., , in : Advances in Modal Logic, Volume 6. : L. : College Publications, 2006. P. 319-332.

Added: February 27, 2013

Kudinov A., Shehtman V. B., , in : Leo Esakia on Duality in Modal and Intuitionistic Logics. : Springer, 2014. Ch. 11. P. 291-334.

We study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces, T1- spaces, dense-in-themselves spaces, a zero-dimensional dense-in-itself separable metric space, R^n (n>1). We also discuss the correlation between languages with different combinations of the ...

Added: March 5, 2014

Schang F., Al-Mukhatabat 2014 Vol. 9 No. 1 P. 230-242

The paper draws attention to the epistemological obstacles that prevented Wittgenstein from acknowledging the modern view of modal logic, including the so-called propositional attitudes. Whilst suggesting a retrospective overview of the logic of epistemic modalities, it is argued that such obstacles primarily rely upon the nature of the logical space depicted in the Tractatus Logico-Philosophicus as well as the ...

Added: October 30, 2014

Zolin E., Logic Journal of the IGPL 2015 Vol. 23 No. 6 P. 861-880

The celebrated theorem proved by Goldblatt and Thomason in 1974 gives necessary and sufficient conditions for an elementary class of Kripke frames to be modally definable. Here we obtain a local analogue of this result, which deals with modal definability of classes of pointed frames. Furthermore, we generalize it to the case of n-frames, which ...

Added: June 14, 2018

Beklemishev L. D., Fernandez-Duque D., Joosten J. J., Studia Logica 2014 Vol. 102 No. 3 P. 541-566

We introduce the logics GLPΛ, a generalization of Japaridze’s polymodal provability logic GLPω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLPω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLPΛ and the decidability of GLPΛ for recursive ...

Added: November 21, 2013