On Lukasiewicz's four-valued modal logic

by

Josep Maria Font (University of Barcelona) and Petr Hájek (Academy of Sciences, Prague)

Studia Logica 70 (2002) 157--182

Abstract

Lukasiewicz's four-valued modal logic is surveyed and analyzed, together with Lukasiewicz's motivations to develop it. A faithful interpretation of it into classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed under the light of the presented results, Lukasiewicz's own texts, and related literature.

 


(A shorter, much preliminary version of this paper was published in Pavel Materna's Festschrift volume:
T. Childers and J. Palomäki (eds.) Between words and worlds(Filosofia, Prague, 2000) 184--198.)