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Journal articles on the topic 'Polymodal logic'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Bell, John L. "Polymodal Lattices and Polymodal Logic." Mathematical Logic Quarterly 42, no. 1 (1996): 219–33. http://dx.doi.org/10.1002/malq.19960420119.

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2

Kracht, Marcus, and Frank Wolter. "Normal monomodal logics can simulate all others." Journal of Symbolic Logic 64, no. 1 (1999): 99–138. http://dx.doi.org/10.2307/2586754.

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AbstractThis paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.

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3

Goldblatt, R. "Algebraic polymodal logic: a survey." Logic Journal of IGPL 8, no. 4 (2000): 393–450. http://dx.doi.org/10.1093/jigpal/8.4.393.

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4

Miyamoto, Sadaaki, Tetsuya Murai, and Yasuo Kudo. "A Family of Polymodal Systems and its Application to Generalized Possibility Measures and Multi-Rough Sets." Journal of Advanced Computational Intelligence and Intelligent Informatics 10, no. 5 (2006): 625–32. http://dx.doi.org/10.20965/jaciii.2006.p0625.

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Polymodal systems generally have large areas of applications to theoretical computer science including the theory of programming, while other applications are not yet fully explored. In this paper we consider a family of polymodal systems with the structure of lattices on the polymodal indices. After investigating theory of the polymodal systems such as the completeness, we study two applications. One is generalized possibility measures in which lattice-valued measures are proposed and relations with the ordinary possibility and necessity measures are uncovered. Second application is considera

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5

Alekseev, P. A., and M. I. Golovanov. "Admissible inference rules for polymodal logicS5 n C." Algebra and Logic 36, no. 5 (1997): 281–87. http://dx.doi.org/10.1007/bf02671605.

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6

Berger, Gerald, Lev D. Beklemishev, and Hans Tompits. "A many-sorted variant of Japaridze’s polymodal provability logic." Logic Journal of the IGPL 26, no. 5 (2018): 505–38. http://dx.doi.org/10.1093/jigpal/jzy012.

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7

MIYAMOTO, Sadaaki. "Polymodal Logic and Application to Systems with Uncertainties of Risks." Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 15, no. 1 (2003): 73–77. http://dx.doi.org/10.3156/jsoft.15.73.

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8

Dashkov, E. V. "On the positive fragment of the polymodal provability logic GLP." Mathematical Notes 91, no. 3-4 (2012): 318–33. http://dx.doi.org/10.1134/s0001434612030029.

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9

Fernández-Duque, David, and Joost J. Joosten. "Models of transfinite provability logic." Journal of Symbolic Logic 78, no. 2 (2013): 543–61. http://dx.doi.org/10.2178/jsl.7802110.

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AbstractFor any ordinal Λ, we can define a polymodal logic GLPΛ, with a modality [ξ] for each ξ < Λ. These represent provability predicates of increasing strength. Although GLPΛ has no Kripke models, Ignatiev showed that indeed one can construct a Kripke model of the variable-free fragment with natural number modalities, denoted . Later, Icard defined a topological model for which is very closely related to Ignatiev's.In this paper we show how to extend these constructions for arbitrary Λ. More generally, for each Θ, Λ we build a Kripke model and a topological model , and show that is sound

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10

Wolter, Frank, and Michael Zakharyaschev. "Decidable fragments of first-order modal logics." Journal of Symbolic Logic 66, no. 3 (2001): 1415–38. http://dx.doi.org/10.2307/2695115.

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AbstractThe paper considers the setof first-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using a mosaic technique, we prove a general satisfiability criterion for formulas in, which reduces the modal satisfiability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragments of various modal predicate logics.

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11

Kracht, Marcus, and Frank Wolter. "Properties of independently axiomatizable bimodal logics." Journal of Symbolic Logic 56, no. 4 (1991): 1469–85. http://dx.doi.org/10.2307/2275487.

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In monomodal logic there are a fair number of high-powered results on completeness covering large classes of modal systems; witness for example Fine [74], [85] and Sahlqvist [75]. Monomodal logic is therefore a well-understood subject in contrast to polymodal logic, where even the most elementary questions concerning completeness, decidability, etc. have been left unanswered. Given that in many applications of modal logic one modality is not sufficient, the lack of general results is acutely felt by the “users” of modal logics, contrary to logicians who might entertain the view that a deep und

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12

AGUILERA, JUAN P., and DAVID FERNÁNDEZ-DUQUE. "STRONG COMPLETENESS OF PROVABILITY LOGIC FOR ORDINAL SPACES." Journal of Symbolic Logic 82, no. 2 (2017): 608–28. http://dx.doi.org/10.1017/jsl.2017.3.

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AbstractGiven a scattered space $\mathfrak{X} = \left( {X,\tau } \right)$ and an ordinal λ, we define a topology $\tau _{ + \lambda } $ in such a way that τ+0 = τ and, when $\mathfrak{X}$ is an ordinal with the initial segment topology, the resulting sequence {τ+λ}λ∈Ord coincides with the family of topologies $\left\{ {\mathcal{I}_\lambda } \right\}_{\lambda \in Ord} $ used by Icard, Joosten, and the second author to provide semantics for polymodal provability logics.We prove that given any scattered space $\mathfrak{X}$ of large-enough rank and any ordinal λ > 0, GL is strongly complete fo

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13

Beklemishev, Lev Dmitrievich. "On the unification problem for $\mathrm{GLP}$." Известия Российской академии наук. Серия математическая 89, no. 1 (2025): 3–17. https://doi.org/10.4213/im9592.

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We show that the polymodal provability logic $\mathrm{GLP}$, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula $[1]p$ does not have maximal unifiers, and exhibit an infinite complete set of unifiers for it. Further, we discuss the algorithmic problem of whether a given formula is unifiable in $\mathrm{GLP}$ and remark that this problem has a positive solution. Finally, we state the arithmetical analogues of the unification and admissibility problems for $\mathrm{GLP}$ and formulate a number of open questions.

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14

Beklemishev, Lev Dmitrievich. "On the unification problem for $\mathrm{GLP}$." Izvestiya: Mathematics 89, no. 1 (2025): 1–14. https://doi.org/10.4213/im9592e.

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We show that the polymodal provability logic $\mathrm{GLP}$, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula $[1]p$ does not have maximal unifiers, and exhibit an infinite complete set of unifiers for it. Further, we discuss the algorithmic problem of whether a given formula is unifiable in $\mathrm{GLP}$ and remark that this problem has a positive solution. Finally, we state the arithmetical analogues of the unification and admissibility problems for $\mathrm{GLP}$ and formulate a number of open questions.

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15

Alexandrov, Islam A., Vladimir Zh Kuklin, Leonid M. Chervyakov, and Sergei A. Sheptunov. "Development of a Technique for Discrete-Logical Decision-Making in Medical Information Systems." HighTech and Innovation Journal 5, no. 4 (2024): 1008–23. https://doi.org/10.28991/hij-2024-05-04-010.

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One of the urgent directions in solving medical diagnostic tasks is to develop new and improved decision support systems capable of efficiently processing polymodal data. Humans cannot always process large arrays of medical information and determine an accurate diagnosis in complex situations. Thus, improving the functioning of the industry requires implementing a variety of systems capable of supporting decision-making of one kind or another. The presented technique aims to steadily increase the level and speed, and demonstrate the feasibility of integrating non-classical logic into the struc

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16

Wolter, F. "The product of converse PDL and polymodal K." Journal of Logic and Computation 10, no. 2 (2000): 223–51. http://dx.doi.org/10.1093/logcom/10.2.223.

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17

Sakai, Hiroshi, and Masahiro Inuiguchi. "Special Issue on Rough Sets and Granular Computing." Journal of Advanced Computational Intelligence and Intelligent Informatics 10, no. 5 (2006): 605. http://dx.doi.org/10.20965/jaciii.2006.p0605.

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Rough sets and granular computing, known as new methodologies for computing technology, are now attracting great interest of researchers. This special issue presents 12 articles, and most of them were presented at the second Japanese workshop on Rough Sets held at Kyushu Institute of Technology in Tobata, Kitakyushu, Japan, on August 17-18, 2005. The first article studies the relation between rough set theory and formal concept analysis. These two frameworks are analyzed and connected by using the method of morphism. The second article introduces object-oriented paradigm into rough set theory,

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18

Dli, Maksim, Andrey Puchkov, Artem Vasiliev, Elena Kirillova, Yuri Selyavskiy, and Nikolay Kulyasov. "Intelligent Control System Architecture for Phosphorus Production from Apatite-Nepheline Ore Waste." Energies 14, no. 20 (2021): 6469. http://dx.doi.org/10.3390/en14206469.

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This paper proposes multilevel architecture for an intelligent control system for the complex chemical energy technological process of yellow phosphorus production from apatite-nepheline ore processing waste. The research revealed that, when controlling this process, one has to deal with large amounts of multiformat and polymodal information, and control goals differ at different levels not only in effectiveness criteria, but also in the structuredness of the level problems. On this basis, it is proposed that intelligent methods be used for the implementation of information processes and contr

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19

de Freitas, Renata, and Petrucio Viana. "Introducing Polymodal Neighbourhood Logics." Electronic Notes in Theoretical Computer Science 247 (August 2009): 51–66. http://dx.doi.org/10.1016/j.entcs.2009.07.048.

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20

Kravtsov, A. G. "Polymodal Logics of Commuting Functions." Logic Journal of IGPL 10, no. 5 (2002): 517–33. http://dx.doi.org/10.1093/jigpal/10.5.517.

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21

Boolos, George. "The analytical completeness of Dzhaparidze's polymodal logics." Annals of Pure and Applied Logic 61, no. 1-2 (1993): 95–111. http://dx.doi.org/10.1016/0168-0072(93)90200-w.

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22

D'Agostino, G., A. Montanari, and A. Policriti. "A set-theoretic translation method for polymodal logics." Journal of Automated Reasoning 15, no. 3 (1995): 317–37. http://dx.doi.org/10.1007/bf00881803.

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23

Дружинин, Андрей Сергеевич. "Irreality and counterfactual thinking in the semiotics of cinema: A cognitive-psychological aspect." ΠΡΑΞΗMΑ. Journal of Visual Semiotics, no. 3(41) (September 20, 2024): 58–90. http://dx.doi.org/10.23951/2312-7899-2024-3-58-90.

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Моделирование возможных миров, альтернативных реальностей и параллельных вселенных по праву можно считать одним из самых востребованных приемов создания художественного образа в литературе и кинематографе. Возможность увидеть жизнь в нескольких вариантах своего развития одновременно, «отменить» принятое решение или переписать историю закладывается в основу захватывающих сюжетов книг и кино. Тем не менее в научной литературе, посвященной логическому и языковому анализу контрфактуальных высказываний и ирреальности, нет достаточного объяснения эмпирических оснований и когнитивно-процедурных механ

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24

KRAVCHUK, Nataliya, and Oleh LUTSYSHYN. "FINANCIAL DIPLOMACY IN INTERDISCIPLINARY DISCOURSE." WORLD OF FINANCE, no. 2(67) (2021): 129–45. http://dx.doi.org/10.35774/sf2021.02.129.

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Introduction. Global transformation processes, the globalization of the financial sphere in particular, which have intensified at the turn of the XX – XXI centuries, created new preconditions for the economization of international relations and the expansion of classical diplomatic tools (including economic and financial) for the foreign policy of individual actors in international relations. Orthodox approaches are being replaced by the realization that financial diplomacy is the basis for forming the economic image of the state; the institution of promoting national interests outside states

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25

Volovyk, A. "ADAPTIVE ESTIMATION OF AIRCRAFT MOVEMENT PARAMETERS IN THE MODE OF THE SET LANDING PATH TRAJECTORY." Information and communication technologies, electronic engineering 2, no. 2 (2022): 67–78. http://dx.doi.org/10.23939/ictee2022.02.067.

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The creation of a large number of new aircraft types and their intensive operation have led to an increase in air traffic. Guaranteeing the required level of safety requires continuous improvement of air traffic organization and control systems. This stimulates the modernization of existing and the creation of new types of radio equipment. In this work, the object of study is the processes of converting information signals in the goniometric channel of the radio landing system, and its goal is to achieve increased accuracy of angular measurements and their reliability by methods of secondary s

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26

SHAPIROVSKY, ILYA B. "SUFFICIENT CONDITIONS FOR LOCAL TABULARITY OF A POLYMODAL LOGIC." Journal of Symbolic Logic, January 27, 2025, 1–26. https://doi.org/10.1017/jsl.2024.62.

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Abstract On relational structures and on polymodal logics, we describe operations which preserve local tabularity. This provides new sufficient semantic and axiomatic conditions for local tabularity of a modal logic. The main results are the following. We show that local tabularity does not depend on reflexivity. Namely, given a class $\mathcal {F}$ of frames, consider the class $\mathcal {F}^{\mathrm {r}}$ of frames, where the reflexive closure operation was applied to each relation in every frame in $\mathcal {F}$ . We show that if the logic of $\mathcal {F}^{\mathrm {r}}$ is locally tabular

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27

Rybakov, Mikhail, and Dmitry Shkatov. "Complexity of finite-variable fragments of products with K." Journal of Logic and Computation, October 22, 2020. http://dx.doi.org/10.1093/logcom/exaa060.

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Abstract We show that products and expanding relativized products of propositional modal logics where one component is the minimal monomodal logic K are polynomial-time reducible to their single-variable fragments. Therefore, the known lower-bound complexity and undecidability results for such logics are extended to their single-variable fragments. Similar results are obtained for products where one component is a polymodal logic with a K-style modality; these include products with propositional dynamic logics.

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28

Rybakov, Mikhail, and Dmitry Shkatov. "Complexity of finite-variable fragments of products with non-transitive modal logics." Journal of Logic and Computation, January 17, 2022. http://dx.doi.org/10.1093/logcom/exab080.

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Abstract We show that products of propositional modal logics where at least one factor is one of the monomodal logics $\textbf {K}$, $\textbf {KT}$, $\textbf {KB}$ and $\textbf {KTB}$ are polynomial-time embeddable into their single-variable fragments. Consequently, we obtain results about the computational complexity of single-variable fragments of logics belonging to intervals bounded by such products. We generalize our embeddability results to expanding relativized products and to products with polymodal logics.

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29

Emmerson, Parker. "Anterolateral Lite 2." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15510371.

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The \emph{Anterolateral Lite 2} formalism arises from a need to robustly track analytic and symbolic distinctions that are often lost in traditional algebraic and geometric frameworks, especially in contexts involving multi-branched solutions and subtle phase phenomena, such as Lorentzian and radical expressions. Classical algebraic structures, which treat coordinates as atomic or globally coherent entities, are prone to \emph{branch collapse}: the unwanted identification of distinct solution branches through singularities, degenerate loci, or insufficiently expressive type systems. Building o

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