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

摘要

The aim of this paper is to introduce an alternative to Lukasie- wicz's 4-valued modal logic L. As it is known, ? is afflicted by "Lukasiewicz (modal) type paradoxes". The logic we define, P?4, is a strong para- consistent and paracomplete 4-valued modal logic free from this type of paradoxes. P?4 is determined by the degree of truth-preserving conse- quence relation defined on the ordered set of values of a modification of the matrix ML characteristic for the logic L. On the other hand, P?4 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. Mathematics Subject Classification. Primary 03B47; Secondary 03B45, 03B50, 03B53.