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Gamma graph calculi for modal logics
Synthese. 2017. Vol. 195. No. 8. P. 3621–3650.
Ma M., Pietarinen A.
We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic.
Bobrova A., Волынская К. А., Праксема. Проблемы визуальной семиотики 2026 Т. 48 № 2 С. 212–235
Musical notation has enjoyed universal recognition for centuries, whereas dance notation has remained comparatively underdeveloped and conceptually challenging. As a kinetic and embodied art form, dance requires a system of notation capable of reflecting its visual, affective, and technical dimensions while at the same time meeting the normative demands of stage practice. The first serious ...
Added: June 2, 2026
Fedyanin D., , in: 17th International Conference, SCSM 2025, Held as Part of the 27th HCI International Conference, HCII 2025, Gothenburg, Sweden, June 22–27, 2025, Proceedings, Part II. Social Computing and Social Media. LNCS, volume 15787Vol. 2.: Switzerland: Springer, 2025. P. 247–256.
The paper proposes a formal model for describing opinions and higher-order opinions (e.g., opinions about opinions) using classical epistemic logic, such as the Kripke structure. Traditionally employed for analyzing knowledge and beliefs, this model is adapted to interpret opinions as beliefs, which is particularly promising for describing human-computer interaction due to its high level of formalization. The study is ...
Added: December 13, 2025
Fedyanin D., Switzerland: Springer, 2025.
The 17th International Conference on Social Computing and Social Media (SCSM 2025)
was an affiliated conference of the HCI International (HCII) conference. It provided an
established international forum for the exchange and dissemination of scientific information related to social computing and social media, addressing a broad spectrum of
issues expanding our understanding of current and future issues in ...
Added: December 3, 2025
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
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
Bobrova A., Праксема. Проблемы визуальной семиотики 2024 № 2(40) С. 32–56
Проводится параллель между логической теорией Ч. Пирса – теорией экзистенциальных графов, и психологической теорией Ф. Джонсона-Лэрда – теорией ментальных моделей. В свое время теория экзистенциальных графов оказала заметное влияние на становление теории ментальных моделей, однако возможности их сотрудничества исчерпаны не были. В работе дается краткая характеристика обеих теорий, а также разбираются аспекты, в которых они ...
Added: August 27, 2024
Dolgorukov V., Popova E., , in: Logic Colloquium 2023, European Summer Meeting of the Association for Symbolic Logic, University of Milan, Italy 5—9 June 2023, Book of Abstracts.: Milan: University of Milan, 2023. P. 90–90.
We present a multi-agent logic for reasoning about knowledge in time which involves delays in the agent’s awareness. Awareness framework divides a common epistemic concept of knowledge into explicit and implicit ones. This division helps to avoid the problem of logical omniscience and proposes new instruments for analysis of resourcebounded agents reasoning. ...
Added: November 26, 2023
Dolgorukov V., Gladyshev M., , in: SCAN 2023 Semantical and Computational Aspects of Non-Classical Logics: Moscow + Online, June 13–17, 2023. Abstracts.: M.: ., 2023. P. 20–23.
This abstract is based on recent work in [6]. We present a static (ELbc) and dynamic (DELbc) epistemic logic for budget-constrained agents. ELbc extends a standard multi-agent epistemic logic with expressions concerning agent’s budgets and formulas’ costs. DELbc extends ELbc with dynamic modality “[?iA]φ” which reads as “φ holds after i’s question whether a propositional ...
Added: November 26, 2023
Pietarinen A., Cognitive Semiotics 2021 Vol. 14 No. 1 P. 29–46
Pragmaticism states that general rules of action, or habits, are generalizing tendencies that lead us to action in conceivable situations describable in general terms. As a method of ‘putting questions to our minds,’ it assigns meanings to signs in terms of conceivable practical consequences for rational conduct. Questions are experiments on various ways of finding ...
Added: August 26, 2023
Bobrova A., Pietarinen A., Pragmatics and Cognition 2022 Vol. 29 No. 1 P. 111–134
Mercier and Sperber (MS) have ventured to undermine an age-old assumption in logic, namely the presence of premise-conclusion structures, in favor of two novel claims: that reasoning is an evolutionary product of a reason-intuiting module in the mind, and that theories of logic teach next to nothing about the mechanisms of how inferences are drawn ...
Added: October 31, 2022
Bobrova A., Pietarinen A., , in: Software Engineering and Formal Methods: SEFM 2019 Collocated Workshops: CoSim-CPS, ASYDE, CIFMA, and FOCLASA, Oslo, Norway, September 16–20, 2019, Revised Selected PapersVol. 12226: Software Engineering and Formal Methods.: Champaign: Springer, 2020. P. 195–205.
Dual-process theories of reasoning take for granted the fundamental difference between the two cognitive systems, Systems 1 and 2. This paper, in contrast, argues that System 1, which is responsible for fast, intuitive, associative, and effortless reasoning, can be explained to be just as logical as System 2, which is said to draw consequences in ...
Added: October 20, 2022
Popova E., Логико-философские штудии 2022 Vol. 20 No. 1 P. 1–7
There are two approaches to merging temporal and epistemic models. The first one consists in starting with a temporal model and enriching it with epistemic dimension (as temporal epistemic logic), while the second one is supposed to start with an epistemic model introducing temporal dimension (dynamic epistemic logic, epistemic temporal logic). The proposed evolutionary epistemic ...
Added: August 1, 2022
Dolgorukov V., Maksim Gladyshev, , in: Dynamic Logic. New Trends and Applications. 4th International Workshop, DaLí 2022, Haifa, Israel, July 31–August 1, 2022, Revised Selected PapersVol. 13780.: Cham: Springer, 2023. P. 56–72.
We present a static (ELbc) and dynamic (DELbc) epistemic logic for budget-constrained agents, in which an agent can obtain some information in exchange for budget resources. ELbc extends a standard multi-agent epistemic logic with expressions concerning agent’s budgets and formulas’ costs. DELbc extends ELbc with dynamic modality “[?iA]φ” which reads as “φ holds after i’s ...
Added: July 31, 2022
В.В. Долгоруков, Логические исследования 2022 Т. 28 № 1 С. 9–26
Implicit group knowledge (or distributive knowledge) is the sum of the knowledge in a group. In this paper, two approaches to group implicit knowledge are compared. According to the first approach, group implicit knowledge is defined as a logical consequence of individual agents’ knowledge sets. According to the second approach, group implicit knowledge is characterized ...
Added: May 16, 2022
Bellucci F., Liu X., Pietarinen A., Logique et Analyse 2020 No. 251 P. 261–296
Peirce’s linear versions of the language of his Existential Graphs (EGs), presented in 1902, are examined. Differences between linear and non-linear languages are explained by permutational invariance and type- vs. occurrence-referentiality: Standard EGs are permutationally invariant with respect to linear EGs, while the Beta part of the system, which corresponds to first-order quantificational theory with ...
Added: December 11, 2021
Carrara M., Chiffi D., Pietarinen A., Logique et Analyse 2020 No. 251 P. 297–315
The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, ...
Added: December 11, 2021
Dolgorukov V., В кн.: Двенадцатые Смирновские чтения: материалы Международной научной конференции, Москва, 24–26 июня 2021 г.: М.: Русское общество истории и философии науки, 2021. С. 86–89.
The paper shows that the concept of distributive knowledge and the concept of implicit knowledge are equivalent in the class of finite distinguishable Kripke models. Some modifications of implicit knowledge are considered. It is demonstrated that these modifications are equivalent in the class of finite distinguishable Kripke models. ...
Added: June 28, 2021
Popova E., , in: Двенадцатые Смирновские чтения: материалы Международной научной конференции, Москва, 24–26 июня 2021 г.: М.: Русское общество истории и философии науки, 2021. P. 134–137.
This paper is concerned with the formalization problem of a wide range of scenarios of how knowledge evolves over time. We focus on combinations of temporal and epistemic modalities reflecting various properties of rational agents’ deliberation. For this purpose, we introduce the model EEM – evolutionary epistemic model. ...
Added: June 28, 2021
Pietarinen A., Beni M., Biosemiotics 2021
The background target of the research going into the present article is to forge an intellectual alliance between, on the one hand, active inference and the free-energy principle (FEP), and on the other, Charles S. Peirce’s theory of semiotics and pragmatism. In the present paper, the focus is on the allegiance between the nomenclatures of active and abductive inferences ...
Added: May 17, 2021
Pietarinen A., Bellucci F., Chiffi D., IfCoLoG Journal of Logics and their Applications 2021 Vol. 8 No. 2 P. 353–376
Assertive graphs (AGs) modify Peirce’s Alpha part of Existential Graphs (EGs). They are used to reason about assertions without a need to resort to any ad hoc sign of assertion. The present paper presents an extension of propositional AGs to the Beta case by introducing two kinds of non-interdefinable lines. The absence of polarities in ...
Added: April 22, 2021
Bobrova A., Эпистемология и философия науки 2020 Т. 57 № 3 С. 176–189
Finally, the first book started Peirceana. Peirceana is expected as a new series that provides access to both Peirce’s mostly unpublished late works and secondary papers, in which ideas of this American philosopher are developed. This edition is opened with three volumes on Peirce’s manuscripts on “Logic of the Future.” The thinker gave this definition ...
Added: April 19, 2021