Institute of Philosophy
of the Russian Academy of Sciences

  Logical Investigations, 2016, Vol. 22, No. 2.
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Logical Investigations, 2016, Vol. 22, No. 2.





N.L. Arkhiereev. Set-theoretic Semantics for Heyting’s System Int

The article aims at analysis of the new method of construction of set-theoretic semantics for Lewis‘s systems S4, S5, which doesn‘t use such notions as ‘possible world’ and ‘model structure’. The initial idea is to interpret each elementary proposition occurring in some formula in the terms fN;C; Ig, i.e. as logically true, logically indeterminate, logically impossible. Such restrictions of possible truth values of the variables of some formula lead to certain restrictions of the original set of state descriptions (s.d.) for the formula, namely on the basis of metavaluations fN;C; Ig restricted, additionally and relatively restricted sets of state descriptions (RSSD, ARSSD, RRSSD respectively) are constructed. These sets substitute model structures of the semantics of possible worlds. The possible world is interpreted as classical s.d. The proposed semantics involves only traditional logical notions such as truth, false, (in)compatibility of the truth values of elementary propositions etc. Besides that the number of RSSD, ARSSD, RRSSD for the formula is always finite. The algorithms of characterization and enumeration of such constructions for the formula are proposed in the article. On the basis of the translation of formulae Int into S4 implemented by McKinsey, Tarski set-theoretic semantics of the same sort for Int is also proposed. The possible world in this semantics is interpreted as classical s.d, and model structures are substituted by finite ordered sets of s.d. Sense of intuitionistic logical connectives is modeled by classical metalanguage with quantifires over s.d. and their sets.

Keywords: modal logic, intuitionistic logic, model structure, set of state-descriptions

DOI: 10.21146/2074-1472-2016-22-2-9-26


L.Yu. Devyatkin. Non-classical Modifications of Many-valued Matrices of the Classical Propositional Logic. Part I.

This paper constitutes the first part of the duology dedicated to many-valued matrices of the classical propositional logic regarded as a tool of construction and analysis of non-classical logics, and it is for the most part of the survey nature. First, I analyze the three approaches to the question when a many-valued matrix defines the classical propositional logic, which are based on the notions of theory, logical consequence relation with single conclusions and multiple-conclusion consequence relation. Then I deal with the matrices of non-classical logics which are functional extensions of classical matrices. The examples of individual matrices of this kind, as well as some classes of them, are considered, some of them known in the literature, and some completely new. Their functional properties are investigated. Among the examples considered are the matrices of three-valued logics of Post,  Lukasiewicz, Bochvar and others. Moreover, I explore a class of matrices which define logics of formal inconsistency (LFI). On the basis of duality between paraconsistent and paracomplete logics, a class of matrices which define logics of formal uncertainty is constructed. Furthermore, I develop a class of four-valued matrices which combine formal inconsistency and formal uncertainty. In the concluding part of the paper I investigate another class of matrices, defining paraconsistent logics which are not logics of formal inconsistency.

Keywords: many-valued logics, logical matrices, paraconsistency, paracompleteness, closed classes of functions

DOI: 10.21146/2074-1472-2016-22-2-27-58




E.G. Dragalina-Chernaya. The Roots of Logical Hylomorphism

The main purpose of this paper is to discuss the origin and the bounds of the schematic hylomorphism in ancient and medieval logic. The sub-purposes are fourfold. Firstly, various explications of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate certain interpretations of Aristotle’s syllogistic. I attempt to answer the question why Aristotle was not the founder of logical hylomorphism. Thirdly, I aim to qualify the schematic hylomorphism of Alexander of Aphrodisias. Finally, I focus on the medieval discussions on syncategoremata and formal consequences.

Keywords: logical hylomorphism, logical form, logical matter, syllogistic, categorematic term, syncategorematic term, material consequence

DOI: 10.21146/2074-1472-2016-22-2-59-72


D. Tiskin. Transparent Readings and Privileged Worlds

I present a problem for Sauerland’s [24] account of the restrictions on certain nonstandard de re readings in propositional attitude reports. Sauerland’s idea is to postulate the ontological prominence of the actual world so that no merely possible individual could have an actual counterpart. However, the problem Sauerland aims to solve extends to multiply nested attitude reports, where his prominence considerations are insufficient to explain either attested or non-attested readings. A solution I propose involves switching to tree-like possible world frames, thus creating an infinity of ontological levels. A remedy for Sauerland’s problem, the approach is shown to have shortcomings as regards the definability of factivity.

Keywords: propositional attitude reports, de dicto, de re, possible worlds, counterpart semantics, tree frames

DOI: 10.21146/2074-1472-2016-22-2-73-90




O.Yu. Goncharko, Ya.A. Slinin, D.A. Chernoglazov. Theodoros Prodromos Logical Works: “Xenedemos and Voices”

This article is the one from our series of articles on the logical texts of Theodoros Prodromos, the Byzantine author of the XII century.We consider to discuss a dialogue «Xenedemos or voices» written in the tradition of platonic dialogue and dedicated to the analysis of the five voices (predicabilia) definitions made by Porphyry in «Isagoge». This text have not yet been translated into any of the modern scientific languages and it is not investigated both in historical and logical scientific literature as well as in the studies of Byzantine literature of the XII century. Nevertheless the ideas of Theodoros Prodromos are interesting in historical, logical, philosophical and literature development perspectives. The purpose of the article is to make a presentation of logical puzzles of Theodoros Prodromos, as well as to offer some outlines of their possible solutions.

Keywords: history of logic, medieval logic, XI–XII century byzantine philosophy

DOI: 10.21146/2074-1472-2016-22-2-91-122

N.Kh. Orlova, S.V. Soloviev. On the History of Logic in Russia Before Revolution: Strategies of Academic Interaction

Some questions of emergence and development of logical studies in Russia before Revolution are considered from the point of view of communication between scholars. A historical retrospective is reconstructed, that includes the peculiar canon applied to the educational literature in logic, the first steps of the tradition of scientific references, the practice to publish critical books in answer to publications by colleagues. Different kinds of publications are considered (translations, textbooks, monographs etc.) For Russian logicians books were a space for discussion and exchange, also with international scientific community. The interaction with other sciences such as psychology and mathematics, and gradual emancipation of logic are outlines. In particular it is considered the influence on the development of Russian logic of so called revolution in mathematics. The paper is based on multiple sources never reprinted after original publication

Keywords: Vasiliev history of logic, mathematics, academic community, strategies of communication, publication activity, referencing

DOI: 10.21146/2074-1472-2016-22-2-123-154


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