• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Book chapter
  • Neighbourhood Frame Product KxK
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
September 25, 2026
AI Users Earn Up to 41.8% More Than Non-Users
Research conducted by economists at HSE University has revealed a significant correlation between the regular use of GenAI in the workplace and higher pay among Russian employees. The study found that individuals who frequently use GenAI in their professional activities earn notably more than those who reject these new tools or resort to them occasionally. The salary premium for highly qualified specialists reaches 41.8%. The article was published in the Voprosy Ekonomiki journal.
September 24, 2026
‘Feedback and Constructive Criticism Are Essential in Our Profession
Vincent Fardeau, Associate Professor at HSE ICEF, has reached a major career milestone: he recently published his paper ‘Asymmetric Thin Markets’ in the Journal of Financial Economics, successfully passed his major academic review, and received tenure. In this interview, Vincent discusses the story behind the paper, explains the concept of asymmetric thin markets, and shares his advice for young scholars aiming to publish in top-tier journals.
September 22, 2026
Personal Interest in Doctoral Thesis Topic Most Important for Confidence in Successful Defence
A researcher at HSE University analysed data on 1,539 doctoral students from 161 Russian universities to identify which features of a thesis topic are associated with academic success and engagement. The most important factor was found to be personal interest in the research topic, which was associated with almost all key aspects of doctoral programme experience—from engaging with the academic supervisor to research activity and confidence about successfully defending the thesis. The findings have been published in Higher Education.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Neighbourhood Frame Product KxK

P. 373–386.
Kudinov A.

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

Language: English
Text on another site
Keywords: modal logicproduct of modal logics

In book

Advances in Modal Logic. Volume 10
Advances in Modal Logic. Volume 10
College Publications, 2014.
Similar publications
Modal Products and Around
Shehtman V. B., Gagarin A., , in: Graph Games and Logic Design. Recent Developments and Further Directions. (TREN, volume 66)Vol. 66.: Springer, 2026. Ch. 17 P. 419–450.
The chapter contains an overview of results on products of propositional modal logics and related constructions: semiproducts, Segerberg squares, and others. We focus mainly on axiomatizations, finite model property, and decidability; we also sketch connections with classical and modal predicate logics. In some cases we give ideas of proofs, especially of those using games. ...
Added: June 30, 2026
Graph Games and Logic Design. Recent Developments and Further Directions. (TREN, volume 66)
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Products of Horn modal logics
Гагарин А. А., , in: Advances in Modal Logic 2024. Short Papers.: [б.и.], 2024. P. 21–26.
We study products of unimodal logics characterized by classes of Kripke frames defined by universal Horn formulas, classifying them with respect to the finite model property (FMP). Further, we show that products of modal logics defined only with variable-free axioms have the FMP. We also provide a partial result regarding products of logics with both Horn and variable-free axioms. ...
Added: August 15, 2024
Advances in Modal Logic 2024. Short Papers
[б.и.], 2024.
The book contains short papers presented at AiML 2024. ...
Added: August 15, 2024
Advances in Modal Logic
College Publications, 2024.
Advances in Modal Logic (AiML) is an initiative founded in 1995 and aimed at presenting an up-to-date picture of the state of the art in modal logic and its many applications. It consists of a conference series together with volumes based on the conferences. The conference series is the main international forum at which research ...
Added: August 14, 2024
Variations on the Kripke trick
Rybakov M., Shkatov D., Studia Logica 2025 Vol. 113 P. 1–48
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
Algorithmic properties of modal and superintuitionistic logics of monadic predicates over finite Kripke frames
Rybakov M., Shkatov D., Journal of Logic and Computation 2025 Vol. 35 No. 2 Article exad078
We show that the monadic modal logic of a single Kripke frame with finitely many possible worlds, but possibly infinite domains, is decidable. This holds true even for monadic multimodal logics with equality, both if equality interpreted as identity and if equality interpreted as congruence. ...
Added: November 3, 2023
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
On Strictly Positive Fragments of Modal Logics with Confluence
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
Correction to: Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter
Rybakov M., Shkatov D., Studia Logica 2021
Added: January 24, 2022
Nāgārjunian-Yogācārian Modal Logic versus Aristotelian Modal Logic
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
Modal logics with transitive closure: Completeness, decidability, filtration
Kikot S., Shapirovsky I., Zolin E., , in: Advances in Modal LogicVol. 13.: College Publications, 2020. P. 369–388.
We give a sufficient condition for Kripke completeness of modal logics that have the transitive closure modality. More precisely, we show that if a modal logic admits what we call definable filtration, then its enrichment with the transitive closure modality (and the corresponding axioms) is Kripke complete; in addition, the resulting logic has the finite ...
Added: December 2, 2020
On existence of recursively-enumerable Kripke-complete first-order modal logics that are not Kripke complete with respect to a first-order definable class of frames
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
Segerberg squares of modal logics and theories of relation algebras
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
Larisa Maksimova on Implication, Interpolation, and Definability
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
Local tabularity without transitivity
Shehtman V. B., Shapirovsky I., , in: Advances in Modal LogicVol. 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
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit