On Lukasiewicz's Four-Valued Modal Logic

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Josep Maria Font
Petr Hájek
Title: On Lukasiewicz's Four-Valued Modal Logic
Journal: Studia Logica
Volume 70
Number 2
Pages: 157-182
Year: 2002


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.