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## On completeness of dynamic topological logic

Moscow Mathematical Journal. 2005. Vol. 5. No. 2. P. 477-492.

Springer, 2014

This volume is dedicated to Leo Esakia’s contributions to the theory of modal and intuitionistic systems. Leo Esakia was one of the pioneers in developing duality theory for modal and intuitionistic logics, and masterfully utilizing it to obtain some major results in the area. The volume consists of 10 chapters, written by leading experts, that ...

Added: March 5, 2014

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

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

Kudinov A., Шапировский И. Б., Известия РАН. Серия математическая 2017 Т. 81 № 3 С. 134-159

In this paper we prove the finite model property and decidability
of a family of pretrasitive modal logics of finite height. We construct special partitions (filtrations) of pretransitive
frames of finite height, which implies the finite model property and
decidability of their modal logics. ...

Added: September 4, 2017

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

College Publications, 2014

Volume 10 contains invited and contributed papers from the tenth conference on "Advances in Modal logic," held in Groningen, the Netherlands, in August 2014. ...

Added: November 7, 2014

Shehtman V. B., Успехи математических наук 2016 Т. 71 № 5 С. 185-186

Приводятся новые результаты о локальной табличности модальных и суперинтуиционистских логик высказываний. Кратко изложена техника бисимуляционных игр, применяемая для доказательства этих результатов. ...

Added: March 16, 2017

Lev D. Beklemishev, Annals of Pure and Applied Logic 2014 Vol. 165 No. 1 P. 82-105

We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant ‘true’ by conjunction and diamonds only. The weaker language allows one to interpret the diamonds as the uniform reflection schemata in arithmetic, possibly of unrestricted logical complexity. We formulate an arithmetically complete calculus with ...

Added: November 21, 2013

Rybakov M., Александров К. И., Шкатов Д. П., / ArXiv. Серия arXiv:2112.03833 "arXiv:2112.03833". 2021.

We show that products of propositional modal logics containing the logic of reflexive frames T as a factor are mbeddable into their single-variable fragments. The proof is a simplified version of the proof, to appear, of a similar result for products and expanding relativized products containing as a factor the logic KTB of reflexive and symmetric Kripke frames. ...

Added: December 10, 2021

Rybakov M., Вестник Тверского государственного университета. Серия: Прикладная математика 2018 № 3 С. 81-94

Рассматривается вопрос о возможности эффективного описания ненормальных и квазинормальных предикатных модальных логик, определяемых семантически посредством классов шкал Крипке с выделенными мирами. Доказывается, что любая ненормальная или квазинормальная (в т. ч. нормальная) модальная предикатная логика, полная относительно некоторого первопорядково определимого класса шкал Крипке с выделенными мирами, погружается в классическую логику предикатов. Показано, как построить соответствующее погружение, ...

Added: October 6, 2019

Шуман А. Н., Journal of Indian Philosophy 2021 Vol. 49 P. 467-498

There are two different modal logics: the logic T assuming contingency and the logic K = assuming logical determinism. In the paper, I show that the Aristotelian treatise On Interpretation (Περί ερμηνείας, De Interpretatione) has introduced some modal-logical relationships which correspond to T. In this logic, it is supposed that there are contingent events. The Nāgārjunian treatise Īśvara-kartṛtva-nirākṛtiḥ-viṣṇoḥ-ekakartṛtva-nirākaraṇa has introduced some modal-logical relationships which correspond ...

Added: July 21, 2021

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

This is a chapter in a book dedicated to Leo Esakia’s contributions to the theory of modal and intuitionistic systems. In this chapter 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 ...

Added: November 7, 2014

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

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

Marseille : [б.и.], 2011

Added: February 27, 2013

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

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

Beklemishev L. D., / Cornell University. Series math "arxiv.org". 2013. No. arXiv:1304.4396.

We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant `true' by conjunction and diamonds only. The weaker language allows one to interpret the diamonds as the uniform reflection schemata in arithmetic, possibly of unrestricted logical complexity. We formulate an arithmetically complete calculus with ...

Added: November 22, 2013

L. : College Publications, 2010

Added: February 27, 2013

College Publications, 2016

“Let's be Logical” is a double invitation. Although logic often refers to a disposition of mind that we all share, this disposition might be confused once its theoretical sources are questioned. The present volume offers thirteen articles that address various aspects of the discipline of logic and its methods, notably formalism, the theory of opposition, ...

Added: June 14, 2016

Kudinov A., Шапировский И. Б., Успехи математических наук 2016 Т. 71 № 1 С. 175-176

О финитной аппроксимируемости модальных логик конечной глубины ...

Added: September 4, 2017

Cham : Springer, 2018

This edited volume focuses on the work of Professor Larisa Maksimova, providing a comprehensive account of her outstanding contributions to different branches of non-classical logic. The book covers themes ranging from rigorous implication, relevance and algebraic logic, to interpolation, definability and recognizability in superintuitionistic and modal logics. It features both her scientific autobiography and original ...

Added: September 20, 2018

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600

We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...

Added: October 25, 2018