Journal of Philosophical Logic 43 (2-3):303-332 (2014)

Authors
José M. Méndez
Universidad de Salamanca
Francisco Salto
Universidad de León
Gemma Robles
Universidad de León
Abstract
Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent.
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DOI 10.1007/s10992-012-9264-0
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References found in this work BETA

Facts and Tautological Entailments.Bas C. Van Fraassen - 1969 - Journal of Philosophy 66 (15):477-487.
The Semantics of Entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
Partiality and its Dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.

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