Possible Worlds as a tool in constructing semantics of certain non-classical logics

Classical logic was formalized and axiomatized in the beginning of the XX century and made it possible to accurately formulate philosophical and methodological premises underlying it. Many of these premises immediately became the subject of criticism and certain revision, which ultimately led to creation of an extensive family of the non-classical logics. Despite the fact that the set of logical systems that today are classified as the non-classical is not just infinite, but continual, all of them could be classified in one of the three main classes. They are logics that consider structural relations between the non-assertoric statements; logics that introduce non-standard models of the propositional functions; logics that include both assertoric and non-assertoric statements. The Lewis’s basic modal systems are related to logical systems of the latter type. They were initially designed to neutralize paradoxes of the material implication, which in classical logic is a model of the deductive logical implication relationship. The Possible Worlds apparatus appears to be the most common way to construct semantics for these systems. The paper analyzes a number of features and formal problems in constructing this kind of semantics.

EDN: ERHIAX

References
[1] Ivlev Yu.V. Kvazimatrichnaya (kvazifunktsionalnaya) logika [Quasi-matrix (quasi-functional) logic]. Moscow, Moscow University Publ., 2018, 16 p.
[2] Ivlev Yu.V. Modalnaya logika [Modal logic]. Moscow, Moscow University Publ., 1991, 224 p.
[3] Feys R. Modal logic. Louvain, E. Nauwelaerts, Paris, 1965 [In Russ.: Feys R. Modalnaya Logika. Moscow, Fizmatlit Publ., 1974, 520 p.].
[4] Hintikka J. Models for Modalities. Selected Essays. Netherlands, D. Reidel Publishing Company, 1969, 220 p.
[5] Priest G. An Introduction to Non-Classical Logic. From If to Is. New York, Cambridge University Press, 2008, 613 p.