Journal of Philosophical Logic (2-3):1-30 (2013)
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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 (by using Dunn semantics) 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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Keywords | Many-valued logic Two-valued under-determined and over-determined interpretations Paraconsistent logics |
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DOI | 10.1007/s10992-012-9264-0 |
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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.
Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
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.
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Citations of this work BETA
Belnap-Dunn Semantics for Natural Implicative Expansions of Kleene's Strong Three-Valued Matrix with Two Designated Values.Gemma Robles & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (1):37-63.
Belnap-Dunn Semantics for Natural Implicative Expansions of Kleene's Strong Three-Valued Matrix II. Only One Designated Value.Gemma Robles, Francisco Salto & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (3):307-325.
Partiality and its Dual in Natural Implicative Expansions of Kleene’s Strong 3-Valued Matrix with Only One Designated Value.Gemma Robles & José M. Méndez - 2019 - Logic Journal of the IGPL 27 (6):910-932.
The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3.Gemma Robles & José M. Méndez - 2020 - Journal of Logic, Language and Information 29 (3):349-374.
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