
70A few more useful 8valued logics for reasoning with tetralattice eightStudia Logica 92 (2). 2009.In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4valued logic to the set 16 to be the powerset of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN 3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, d…Read more

63Bifacial Truth: a Case for Generalized Truth ValuesStudia Logica 101 (6): 12991318. 2013.We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semiclassical neg…Read more

46FirstDegree Entailment and its RelativesStudia Logica 105 (6): 12911317. 2017.We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of firstdegree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it is possible to capt…Read more

42Relevant generalization starts here (and here = 2)Logic and Logical Philosophy 19 (4): 329340. 2010.There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing, is closely connected to the powersetting formation on the base of some initial truth values. Having a set of generalized truth values, one can introduce fundamental logical notions, more specifically, the ones of logical …Read more

39Rational Agency from a TruthFunctional PerspectiveLogic and Logical Philosophy 25 (4): 499520. 2016.The aim of the present paper is to introduce a system, where the epistemic state of an agent is represented truthfunctionally. In order to obtain this system, we propose a fourvalued logic, that we call the logic of rational agent, where the fact of knowing something is formalized at the level of valuations, without the explicit use of epistemic knowledge operator. On the basis of this semantics, a sound and complete system with two distinct truthfunctional negations is provided. These negati…Read more

33A Few More Useful 8valued Logics for Reasoning with Tetralattice EIGHT 4Studia Logica 92 (2): 265280. 2009.In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4valued logic to the set 16 to be the powerset of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, d …Read more

24A Variant of Material Connexive LogicBulletin of the Section of Logic 51 (2): 227242. 2022.The relationship between formal logic and informal 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…Read more

24The Logical Legacy of Nikolai Vasiliev and Modern Logic (edited book)Springer Verlag. 2017.This volume offers a wide range of both reconstructions of Nikolai Vasiliev’s original logical ideas and their implementations in the modern logic and philosophy. A collection of works put together through the international workshop "Nikolai Vasiliev’s Logical Legacy and the Modern Logic," this book also covers foundations of logic in the light of Vasiliev’s contradictory ontology. Chapters range from a look at the Heuristic and Conceptual Background of Vasiliev's Imaginary Logic to Generalized …Read more

22Towards ProtolanguageEpistemology and Philosophy of Science 58 (1): 94111. 2021.In this paper, I attempt to offer a general outline of my views on the origin and evolution of language. I do not pretend in any way to a completely new conception of language evolution. It seems to me that all the most important and productive hypotheses about the origin of language have already been made before, and it is only a matter of putting the pieces of the puzzle together correctly. As far as I can see it, the evolution of language is directly related to the embedded and embodied emoti…Read more

21The FmlaFmla Axiomatizations of the Exactly True and Nonfalsity Logics and Some of Their CousinsJournal of Philosophical Logic 48 (5): 787808. 2019.In this paper we present a solution of the axiomatization problem for the FmlaFmla versions of the Pietz and Rivieccio exactly true logic and the nonfalsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific prooftheoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the res…Read more

18Basic FourValued Systems of Cyclic NegationsBulletin of the Section of Logic 51 (4): 507533. 2022.We consider an example of four valued semantics partially inspired by quantum computations and negationlike operations occurred therein. In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation. We define two variants of logical matrices performing different orders over the set of truth values. Purely formal logical result of our study consists in axiomatizing the logics of defined matric…Read more

Generalized VasilievStyle PropositionsIn Dmitry Zaitsev & Vladimir Markin (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic, Springer Verlag. 2017.

Imaginary logic2: Formal reconstruction of the unnoticed Nikolai vasiliev's logical systemLogique Et Analyse 45 (178): 3954. 2002.
Dmitry Zaitsev
Lomonosov Moscow State University
Moscow State University

Lomonosov Moscow State UniversityProfessor

Areas of Specialization
Science, Logic, and Mathematics 
Logic and Philosophy of Logic 