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Squares of modal logics with additional connectives
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 are proved. A translation of Segerberg squares into classical predicate logic is constructed. Bibliography: 21 titles.
Shehtman V. B., , in : Larisa Maksimova on Implication, Interpolation, and Definability. : Cham : Springer, 2018. P. 245-296.
We establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a corollary we obtain examples of undecidable finitely axiomatizable strictly positive normal modal logics. The translation has its counterpart on the level of proofs: we formulate a natural ...
Added: September 21, 2018
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
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., 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
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
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
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
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
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
L. : College Publications, 2010
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
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
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
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
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
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
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
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
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
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