Advances in Modal Logic. Val. 11.

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Advances in Modal Logic

Vol. 11. L. : College Publications, 2016.

Academic editor: Beklemishev L. D., S. Demri, A. Mate

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, and proof theory.

These proceedings record the papers presented at the 2016 conference on Advances in Modal Logic, a biennial conference series with an aim to report on important new developments in pure and applied modal logic. As indicated above, there are new developments in using modal logic to reason about obligations, about programs, about time, about combinations of modal logics and even about negation itself.

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

Language: English

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Keywords: modal logic модальная логика

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

О кванторной версии модальной логики Белнапа–Данна

Грефенштейн А. В., Speranski S. O., Математический сборник 2024 Т. 215 № 3 С. 37–69

Разрабатывается кванторная версия пропозициональной модальной логики BK из статьи С. П. Одинцова и Х. Вансинга, в основе которой лежит (немодальная) система Белнапа–Данна; мы будем обозначать эту версию через QBK. Сначала с помощью метода канонических моделей будет доказано, что QBK — как и некоторые важные её расширения — сильно полна относительно подходящей семантики возможных миров. Затем мы ...

Added: December 26, 2025

Two Types of Filtrations for wK4 and Its Relatives

Kudinov A., Shapirovsky I., Studia Logica 2025 P. 1–25

We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For m > 0, let Lm be the logic defined by axiom ♦^{m+1}p → ♦p ∨ p. We construct quotient filtrations for the logics Lm, which implies that these logics and their tense counterparts have the finite model property. Then, we construct selective filtrations ...

Added: October 14, 2025

Влияние аксиомы связности на сложность модальной логики.

Kudinov A., Мясников К. М., Математика и теоретические компьютерные науки 2025 Т. 3 № 2 С. 58–84

The paper proves that for weakly transitive logics with the universal modality, whose formula satisfiability problem is in PSPACE, adding the connectedness axiom does not increase the complexity. Furthermore, an explicit algorithm solving this problem is presented. ...

Added: October 14, 2025

Логики с аксиомой конвергентности: сложность при малом числе переменных в языке

Rybakov M., Щербаков М. И., В кн.: Четырнадцатые Смирновские чтения по логике: материалы Междунар. науч. конф., Москва, 19-21 июня 2025 г.: М.: Издатель Александр Воробьев, 2025. С. 46–49.

Логики с аксиомой конвергентности: сложность при малом числе переменных в языке ...

Added: June 21, 2025

Сложность константных фрагментов ненормальных модальных логик

Kudinov A., Rybakov M., В кн.: Четырнадцатые Смирновские чтения по логике: материалы Междунар. науч. конф., Москва, 19-21 июня 2025 г.: М.: Издатель Александр Воробьев, 2025. С. 36–39.

Показано, что каждая модальная логика, содержащая классическую логику высказываний и содержащаяся в слабой логике Гжегорчика, имеет NP-трудную проблему выполнимости для константного фрагмента. В частности, константные фрагменты ненормальных модальных логик E, EM, EN и EMN являются coNP-полными. ...

Added: June 21, 2025

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

Complexity of the variable-free fragment of the weak Grzegorczyk logic

Rybakov M., Агаджанян И. А., / arXiv. Серия 2211.14571 "Logic". 2022.

Доказывается PSPACE-трудность константных фрагментов всех логик, лежащих между K и wGrz ...

Added: December 5, 2022

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

Сложность фрагментов произведений с логикой T в языке с одной переменной

Rybakov M., Aleksandrov K., 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

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