On Łukasiewicz's four-valued modal logic
The aim of this paper is to survey and analyze Łukasiewicz's four-valued modal logic (denoted as Ł). Section 2 presents Łukasiewicz's system Ł, some mathematical results concerning the classification of the system Ł under several standard criteria, and its main semantic and algebraic properties. The authors outline the translation mapping between Ł and the classical propositional calculus (CPC), and prove their basic result (Theorem 1) showing that a formula \(\varphi\in\text{Ł}\) is a tautology if and only if its corresponding formula \(\varphi^*\in\text{CPC}\) does. In Sections 3 and 4, some counter-intuitive aspects of the system Ł are presented and discussed, based on the consequences derived from the obtained results, combined with Łukasiewicz's own texts and the rich related literature.
scientific article; zbMATH DE number 1764808