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On Łukasiewicz's Four-Valued Modal Logic

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Abstract

Łukasiewicz's four-valued modal logic is surveyed and analyzed, together with Łukasiewicz's motivations to develop it. A faithful interpretation of it in 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 in the light of the presented results, Łukasiewicz's own texts, and related literature.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Josep Maria Font

  2. Institute of Computer Science, Academy of Sciences, Pod vodarenskou vezi 2, 182 07, Prague, Czech Republic

    Petr Hájek

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  1. Josep Maria Font
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Font, J.M., Hájek, P. On Łukasiewicz's Four-Valued Modal Logic. Studia Logica 70, 157–182 (2002). https://doi.org/10.1023/A:1015111314455

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