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Н.Л. Архиериев

10

Гуманитарный вестник

# 7·2016

Theory of logical modalities without “possible worlds”

©

N.L. Arkhiereev

Bauman Moscow State Technical University, Moscow, 105005, Russia

The article examines the main problems of “traditional” modal logic semantics — so

called possible worlds semantics. Interpreting modal operators meanings semantics data

involve either the notion of the real world, or the notion of the model structure and the

accessibility relations between the worlds. The last one does not have the monosemantic

interpretation, therefore leads to series of paradoxes. In addition, we have researched the

main principles of the alternative semantics construction for the Lewes system S5 — se-

mantics of restricted set of state-descriptions and relatively restricted sets of state-

descriptions. This semantics uses only the “classical” notions such as state-descriptions,

state-descriptions sets, semantical validity, satisfiability, etc. That is what distinguishes

them from possible world semantics.

Keywords:

modality, possible world, model structure, accessibility relation, restricted set

of state-descriptions, truth, false, validity, satisfiability.

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Arkhiereev N.L.

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Arkhiereev N.L.

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Arkhiereev N.L.

, Cand. Sci. (Philosophy), Assoc. Professor, “Philosophy” Departmen,

Bauman Moscow State Technical University. e-mail:

arkh-nikolaj@yandex.ru