Simplified Kripke-Style Semantics for Some Normal Modal Logics

Pietruszczak, A.; Klonowski, M.; Petrukhin, Y.

Авторы: Pietruszczak Andrzej, Klonowski Mateusz, Petrukhin Yaroslav
Журнал: Studia Logica
Том: 108
Номер: 3
Год издания: 2020
Издательство: Springer Nature
Местоположение издательства: Switzerland
Первая страница: 451
Последняя страница: 476
DOI: 10.1007/s11225-019-09849-2
Аннотация: Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics K45 , KB4 ( =KB5 ), KD45 are determined by suitable classes of simplified Kripke frames of the form ⟨W,A⟩ , where A⊆W . In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of K45 . Furthermore, a modal logic is a normal extension of K45 (resp. KD45 ; KB4 ; S5 ) if and only if it is determined by a set consisting of finite simplified frames (resp. such frames with A≠∅ ; such frames with A=W or A=∅ ; such frames with A=W ). Secondly, for all normal extensions of K45 , KB4 , KD45 and S5 , in particular for extensions obtained by adding the so-called “verum” axiom, Segerberg’s formulas and/or their T-versions, we prove certain versions of Nagle’s Fact (J Symbol Log 46(2):319–328, 1981. https://doi.org/10.2307/2273624) (which concerned normal extensions of K5 ). Thirdly, we show that these extensions are determined by certain classes of finite simplified frames generated by finite subsets of the set N of natural numbers. In the case of extensions with Segerberg’s formulas and/or their T-versions these classes are generated by certain finite subsets of N .
Добавил в систему: Петрухин Ярослав Игоревич

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Simplified Kripke-Style Semantics for Some Normal Modal Logicsстатья

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