Journal of Logic, Language and Information 25 (2):163-189 (2016)
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| Abstract |
Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics.
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| Keywords | Many-valued logics Modal many-valued logics Łukasiewicz many-valued logics Bilattice logics Belnap–Dunn type bivalent semantics |
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| DOI | 10.1007/s10849-016-9237-8 |
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References found in this work BETA
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview.
Aristotle's Syllogistic From the Standpoint of Modern Formal Logic.Jan Łukasiewicz - 1951 - Oxford, England: Garland.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
How a Computer Should Think.Nuel Belnap - 1977 - In G. Ryle (ed.), Contemporary Aspects of Philosophy. Oriel Press.
Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
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Citations of this work BETA
40 Years of FDE: An Introductory Overview.Hitoshi Omori & Heinrich Wansing - 2017 - Studia Logica 105 (6):1021-1049.
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