Alex Belikov

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Elena Lisanyuk

Saint-Petersburg State University

Anatoliy Migunov

Saint-Petersburg State University

David Khizanishvili

Immanuel Kant Baltic Federal University

Alexandra Pavlova

Université Paris 1 - Panthéon-Sorbonne

Igor Berestov

Institute for Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences

Yury Zagorulko

Pavel Butakov

Institute for Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences

Marina Volf

Institute for Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences

Ivan Mikirtumov

National Research University “Higher School of Economics” (HSE), Moscow, Russia

Denis Maslov

National Research University “Higher School of Economics” (HSE), Moscow, Russia

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Papers by Alex Belikov

Modelling Argumentation: Valuations and Reasoning

Vestnik Tomskogo gosudarstvennogo universiteta. Filosofiya, sotsiologiya, politologiya, 2020

Рассматривается проблема формального моделирования аргументации. Выявляются основные характеристи... more Рассматривается проблема формального моделирования аргументации. Выявляются основные характеристики аргументативных рассуждений, играющие ключевую роль в оценке аргументации. Авторы предлагают формальную экспликацию отношения подтверждения между аргументами и тезисом, которая учитывает вариативность отношения следования, т.е. позволяет иметь дело как с дедуктивным, так и с правдоподобным следованием в одном формальном контексте. Ключевые слова: аргументация, аргументативные рассуждения, оценка аргументации, формальные модели аргументации.

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Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion

Logic and Logical Philosophy, 2021

In this paper, we present two variants of Peirce's Triadic Logic within a language containing onl... more In this paper, we present two variants of Peirce's Triadic Logic within a language containing only conjunction, disjunction, and negation. The peculiarity of our systems is that conjunction and disjunction are interpreted by means of Peirce's mysterious binary operations Ψ and Φ from his 'Logical Notebook'. We show that semantic conditions that can be extracted from the definitions of Ψ and Φ agree (in some sense) with the traditional view on the semantic conditions of conjunction and disjunction. Thus, we support the conjecture that Peirce's special interest in these operations is due to the fact that he interpreted them as conjunction and disjunction, respectively. We also show that one of our systems may serve as a suitable base for an interesting implicative expansion, namely the connexive threevalued logic by Cooper. Sound and complete natural deduction calculi are presented for all systems examined in this paper.

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On bivalent semantics and natural deduction for some infectious logics

Logic Journal of the IGPL, 2021

In this work, we propose a variant of so-called informational semantics, a technique elaborated b... more In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s ${\mathbf{S}_{\mathbf{fde}}}$ and Szmuc’s $\mathbf{dS}_{\mathbf{fde}}$. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ are formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for ${\mathbf{S}_{\mathbf{fde}}}$ containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for $\mathbf{dS}_{\mathbf{fde}}$ and to reflect the fundamental symmetry between...

Exactly true and non-falsity logics meeting infectious ones

Journal of Applied Non-Classical Logics, 2020

In this paper, we study logical systems which represent entailment relations of two kinds. We ext... more

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Семантики Войшвилло для некоторых расширений логики FDE: часть I

Logical Investigations, 2018

В настоящей статье исследуются семантики полуобобщенных описаний состояний, которые являются разн... more В настоящей статье исследуются семантики полуобобщенных описаний состояний, которые являются разновидностью информационной семантики Е.К. Войшвилло, предложенной им для первоуровневой релевантной логики $(\textbf{FDE})$ в начале восьмидесятых годов. Ключевой особенностью войшвилловского подхода является рассмотрение описаний состояний, на которые не налагаются классические условия о непротиворечивостии полноте, что позволяет определить релевантное отношение следования. Под релевантным отношением следования понимается такое, для которого не проходят классические парадоксы: $A\wedge{\sim}A\models B$и $B\models A\vee{\sim}A $ . Нами рассматриваются известные расширения логики $(\textbf{FDE})$, сформулированные в терминах систем бинарных следований: трехзначная логика Клини, логика Приста и классическая логика. Первые две из них могут быть семантически определены при помощи полуобобщенных описаний состояний: для логики Клини вводится понятие $\top$-обобщенных описаний состояний (непроти...

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A Variant of Material Connexive Logic

Bulletin of the Section of Logic, 2021

The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning ... more The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version of connexive logic which validates Boethius’ (and thus, Aristotle’s) Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation.

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Modelling Argumentation: Valuations and Reasoning

Vestnik Tomskogo gosudarstvennogo universiteta. Filosofiya, sotsiologiya, politologiya, 2020

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Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion

Logic and Logical Philosophy, 2021

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On bivalent semantics and natural deduction for some infectious logics

Logic Journal of the IGPL, 2021