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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.
REFERENCES
[1]
Sidorenko E.A.
Logika, paradoksy, vozmozhniye miry
[Logic, paradoxes,
possible worlds]. Moscow, URSS Publ., 2002, 310 p.
[2]
Voyshvillo E.K.
Filosofskiye nauki
— Philosophical sciences
, Moscow, 1983,
no. 3, pp. 76–80.
[3]
Kripke S. Semantichesskiy analiz modalnoy logiki [Semantic analysis of modal
logics]. In:. R. Feis.
Modalnaya logika
[Modal logics]. Moscow, Nauka, 1974,
pp. 254–303. [in Russ.].
[4]
Priest G.
An Introduction to Non-Classical Logic: From If to Is.
Cambridge,
Cambridge University Press, 2008, 613 p.
[5]
Ivlev Yu.V.
Modalnaya logika
[Modal logics]. Moscow, MGU Publ., 1991,
pр. 168–190.
[6]
Bocharov V.А., Markin V.I.
Vvedeniye v logiku
[Introduction to logics].
Мoscow, Infra-M Publ., 2008, 354 p.
[7]
Arkhiereev N.L.
Logicheskiye issledovaniya
— Logical Research
, 2010, iss. 16,
pp. 3–22.
[8]
Arkhiereev N.L.
Logiko-filosofskiye issledovaniya — Logic and Philosophical
Research
, 2010, iss. 4, pp. 123–130.
Arkhiereev N.L.
, Cand. Sci. (Philosophy), Assoc. Professor, “Philosophy” Departmen,
Bauman Moscow State Technical University. e-mail:
arkh-nikolaj@yandex.ru