Logical Investigations. Vol. 20. — М.–S.-Pb.: C.G.I., 2014. — 320 p. — ISBN 978-5-98712-197-3.

 Our authors:

• E.K. Voishvillo. To the problem of the justification of apodictic knowledge

A discussion presented in this paper concerns the relationship between the rival views on fundamental problem of apodictic knowledge justification. The ideas reviewed here mostly date back to I. Kant and D. Hilbert. The processes of idealization and abstraction are analized in order to explain a phenomenon of spreading of the idealized and abstract objects throughout the scientific theories and their role in theories’ construction and development.

Keywords: APODICTIC KNOWLEDGE, SCIENTIFIC THEORY, IDEALIZATION, ABSTRACTION, CONCEPT

• D.V. Zaitsev. Dispositionality, enthymeme and knowledge

After a short introduction, in the second section, I consider E. Voishvillo’s approach to formal explication of dispositional predicates. The third section is a brief presentation of relevantly interpreted enthymematic implication. In the forth section I make an attempt to draw all-in-one and present a formalization of (enthymematic) reasoning with (dispositional) public announcements.

Keywords: DISPOSITIONAL PREDICATE, ENTHYMEMATIC IMPLICATION, PUBLIC ANNOUNCEMENT LOGIC

• V.I. Markin. E.K. Voishvillo’s theory of concept: value and prospects

The paper contains the analysis of the Theory of Concept in its modern version worked out by E.K. Voishvillo. Its advances in the study of concept as a form of thought are observed. At the same time some points for further research are marked out.

Keywords: CONCEPT, EXTENSION, INTENSION, GENUS, PREDICATE, THEORY, ENTAILMENT, LOGICAL FORM, FORMALIZED LANGUAGE

• I.B. Mikirtoumov. Ernst Mally’s theory of objects and intensional logic

In the article the object-theoretical logical theory of Ernst Mally is investigated. Considered its non-formal grounds, describes the features of theory, and explores the question of its compliance with the classical propositional logic. For realization of the proposed interpretation of non-trivial implication the intensional logic of object is constructed. The overall conclusion is that the logical theory of the object is Mally submitted the version of the formal semantics.

Keywords: OBJECT THEORY, FORMAL SEMANTICS, ERNST MALLY, INTENSIONAL LOGIC

• N.N. Nepeivoda. Constructive mathematic: review of progress, lacks and lessons. Part III

Constructivist concepts not assuming that we know programs for each effective method (intuitionism et al) are analyzed here.

Keywords: INTUITIONISM, CONSTRUCTIVISM, REALIZABILITY, COMPUTABILITY, APPLICATION OF CONSTRUCTIVISM

• V.M. Popov. Embedding classical propositional logic into paralogics related to Par

The work is carried out in the line with a study of connections between classical logic, on one hand, and non-classical logics, on the other hand. In the paper an effectively computable mapping is constructed that embeds classical propositional logic into any paralogic, which includes logic Par from [2] and has the same language with Par.

Keywords: CLASSICAL PROPOSITIONAL LOGIC, PARACONSISTENT LOGIC, PARACOMPLETE LOGIC, EMBEDDING MAP

• О.V. Popov. The intensional use, appellatio rationis and incomplete object descriptions: an analysis of nonextensional contexts in the works by J. Buridan and Е.К. Voishvillo

This article deals with the content of J. Buridan’s notion appellatio rationis. J. Buridan’s views are juxtaposed with those of Е.К. Voishvillo upon the differences between the intensional and extensional use of linguistic expressions. Here is presented the author’s original approach towards the interpretation of J. Buridan’s conception of intensional contexts, their specific character.

Keywords: APPELLATIO RATIONIS, INTENSIONAL AND EXTENSIONAL USE OF LINGUISTIC EXPRESSIONS, INTENSIONAL CONTEXTS

• N.N. Prelovskiy. Infinite-valued  Lukasiewicz logic and criteria for existence of factor-semantics in multi-valued logics

A concept of local factor-semantics is introduced while constructing matrices K and K', isomorphic to the standard rational-valued matrix for infinite-valued logic of Lukasiewicz.

Keywords: LOGICS OF LUKASIEWICZ, FACTOR-SEMANTICS, LOGICAL MATRICES, ISOMORPHISM, LOCAL FACTOR-SEMANTICS

• V.I. Shalack. Protologic and its structure

The article sets out a generalization of logical to the level of operating signs.

Keywords: PROTOLOGIC, SEMIOTICS, THEORY OF SIGNS, FOUNDATIONS OF LOGIC, COMBINATORY LOGIC, LAMBDA-CALCULUS

• K.I. Bakhtiyarov. Metascience symbols (universal characteristic)

Leibniz called the first article "New method maximums and minimums". Instead of considering the realisation of the method for maximums and minimums, it should have been considered from symbolic side as the Universal characteristic. The extremums as symbols of universal language covers all infinity of the certain subjects sense of which it is. Creation of a block matrix (by means of the left tensor square) allowed to reveal macrolevel and circular arrangement of charts. And in philosophy of a science there is no other way to follow the Nature except to follow to genetics. The logic reduction of a non-classical multi-valuedness to classical binarity of the designated and anti-designated values forms overlaps from right to left and from left to right, forming a hysteresis loop arranging the circular order. The complementarity of levels generates fractality of the main table structure.

Keywords: CHARACTERISTIC, EXTREMUMS, DESIGNATED, ANTI-DESIGNATED VALUES, FRACTALITY, LOGIC REDUCTION

• A.E. Bolotov, V.O. Shangin. Natural deduction in a paracomplete setting

In this paper we present the automated proof search technique in natural deduction paracomplete logic. Here, for some statements we do not have evidence to conclude if they are true or false, as it happens in the classical framework. As a consequence, for example, formulae of the type p ∨ ¬p, are not valid. In this paper we formulate the natural deduction system for paracomplete logic PComp, explain its main concepts, define proof searching techniques and the searching algorithm providing examples proofs.

Keywords: PARACONSISTENT LOGIC, NATURAL DEDUCTION, PROOF SEARCH

• L.Yu. Devyatkin. Three-valued matrices with classical consequence relation for an arbitrary propositional language

In this paper the class of three-valued matrices with classical consequence relations is defined.

Keywords: CLASSICAL PROPOSITIONAL LOGIC, THREE-VALUED LOGICS, CONSEQUENCE RELATION

• A. Tamminga. Correspondence analysis for strong three-valued logic

I apply Kooi and Tamminga’s (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for Lukasiewicz’s three-valued logic.

Keywords: THREE-VALUED LOGIC, CORRESPONDENCE ANALYSIS, PROOF THEORY, NATURAL DEDUCTION SYSTEMS

• Bibliography of “Logical Investigations”

 Our authors:

VOISHVILLO Evgenij Kazimirovich — D.Sc., Soviet and Russian Philosopher and Logician, Honoured Professor of Lomonosov Moscow State University, Lomonosov Prize I degree Winner.
ZAITSEV Dmitry Vladimirovich — D.Sc., Associate Professor, Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University.
MARKIN Vladimir Ilyich — D.Sc., Professor, Head of the Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University.
MIKIRTUMOV Ivan Borisovich — D.Sc., Associate Professor, Head of the Department of Logic, Saint-Petersburg State University.
NEPEIVODA Nikolay Nikolayevich — Doctor of Ph.-Math. Sci, Professor, Leading research scientist, Research Center for Multiprocessor Systems, Program System Institute, Russian Academy of Sciences, Pereslavl-Zalessky.
POPOV Vladimir Mikhailovich — Ph.D., Associate Professor, Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University.
POPOV Oleg Vladilenovich — Lecturer, Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University.
PRELOVSKIY Nikolay Nikolayevich — Ph.D., Research scientist, Department of Logic, Institute of Philosophy, Russian Academy of Sciences.
SHALACK Vladimir Ivanovich — D.Sc., Leading research scientist, Department of Logic, Institute of Philosophy, Russian Academy of Sciences.
BAKHTIYAROV Kamil Ibragimovich — D.Sc. in Philosophy, Ph.D. in Technical Sciences, Professor at the Department of Higher Mathematics of the Goryackin State University of Agricultural Engineering.
DEVYATKIN Leonid Yurievich — Ph.D., Senior research scientist, Department of Logic, Institute of Philosophy, Russian Academy of Sciences.
BOLOTOV Alexander Efimovich — Ph.D., Principal Lecturer, Department of Computer Science and Software Engineering, School of Electronics and Computer Science, University of Westminster, UK.
TAMMINGA Allard — Ph.D., Senior Lecturer, Faculty of Philosophy, Department of Theoretical Philosophy, University of Groningen.
SHANGIN Vasilyi Olegovich — Ph.D., Associate Professor, Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University.

Subscription index under the catalogue «Press of Russia»: 42046. Second half-year period of 2014.

Published materials have undergone the reviewing process.

The yearbook is included in the new list of publications recommended by the Higher assesment commission of Russian Federation for the publication of materials of D.Sc. and Ph.D. dissertational research in the field of philosophy (since 1^st of January 2010).