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## Advances in Modal Logic

Issue 9.
L. :
College Publications, 2012.

Academic editor: T. Bolander, T. Brauner, S. Ghilardi

*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.

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

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

Beklemishev L. D., , in : Advances in Modal Logic. Issue 9.: L. : College Publications, 2012. P. 89-94.

Several interesting applications of provability logic in proof theory made use of a polymodal logic GLP due to Giorgi Japaridze. This system, although de- cidable, is not very easy to handle. In particular, it is not Kripke complete. It is complete w.r.t. neighborhood semantics, however this could only be established recently by rather complicated techniques ...

Added: April 3, 2013

Tiu A., Ianovski E., Goré R., , in : Advances in Modal Logic. Issue 9.: L. : College Publications, 2012. P. 516-537.

A grammar logic refers to an extension of the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal operator [a] comes with a converse [¯a]. Extending previous works on nested sequent systems for ...

Added: February 25, 2019

Priority areas:
mathematics

Language:
English

Keywords: modal logic

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

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

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

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

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

Marseille : [б.и.], 2011

Added: February 27, 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

Vasyukov V. L., Logical Investigations 2013 No. 19 P. 353-365

Recently some elaborations were made concerning the game theoretic semantic of Lℵ0 and its extension. In the paper this kind of semantics is developed for Dishkant’s quantum modal logic LQ which is also, in fact, the speciﬁc extension of Lℵ0 . As a starting point some game theoretic interpretation for the S L system (extending ...

Added: June 21, 2013

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

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., 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

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

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

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

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

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

Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624

Added: February 27, 2013

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70

A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...

Added: July 19, 2014

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 2019

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019