NDLI: A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes

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A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes

Content Provider	Springer Nature Link
Author	Méndez, José M. Robles, Gemma
Copyright Year	2015
Abstract	The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz (modal) type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other hand, PŁ4 is a rich logic in which a number of connectives can be defined. It also has a simple bivalent semantics of the Belnap–Dunn type.
Starting Page	501
Ending Page	522
Page Count	22
File Format	PDF
ISSN	16618297
Journal	Logica Universalis
Volume Number	9
Issue Number	4
e-ISSN	16618300
Language	English
Publisher	Springer Basel
Publisher Date	2015-09-22
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Many-valued logics modal logics paraconsistent logics paracomplete logics 4-valued modal logics Łukasiewicz 4-valued modal logic Belnap–Dunn type semantics Substructural logics Modal logic Many-valued logic Paraconsistent logics Mathematics Computer Science Logic
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Logic

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