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.
['José Manuel Gómez y Méndez', 'Gemma Robles']
A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes