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Н.Л. Архиереев
12
Гуманитарный вестник
# 02·2017
Natural models for iterated modalities in the Lewis' S4 system
© N.L. Arkhiereev
Bauman Moscow State Technical University, Moscow, 105005, Russia
The primary means of interpretation in the case of modal calculi in contemporary logic is
the so-called possible worlds semantics (of the relational and neighbourhood types). In
these semantics, the basic concepts include the possible world, the model structure and
the accessibility relation between possible worlds. Though possible worlds semantics
appear to be more natural than algebraic and topological semantics of modal calculi,
their fundamental concepts lack a meaningful interpretation. The problem of interpreting
iterated modal operators poses a particular challenge. The article describes a fundamen-
tally new approach to developing modal logic semantics, using only their conventional
concepts of logical truth, satisfiability etc. We suggest a natural interpretation of iterated
modalities in the S4 system based on this approach.
Keywords:
modality, possible world, model structure, accessibility relation, relatively
bounded set of state descriptions, true, false, satisfiability, validity
REFERENCES
[1]
Arkhiereev N.L.
Filosofiya nauki — Philosophy of Sciences
, 2010, no. 2 (45),
pp. 78–91.
[2]
Arkhiereev N.L.
Logiko-filosofskie issledovaniya
— Studies in logic and
philosophy
, 2010, issue 4, pp. 123–130.
[3]
Ivlev Yu.V.
Modalnaya logika
[Modal logic]. Moscow, Lomonosov Moscow
State University Publ., 1991, pp. 168–190.
Arkhiereev N.L.
, Cand. Sci. (Philos.), Assoc. Professor, Department of Philosophy,
Bauman Moscow State Technical University. е-mail:
arkh-nikolaj@yandex.ru