Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz's 3-valued Logic Ł3

Journal of Philosophical Logic (2-3):1-30 (2013)
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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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Author Profiles

Gemma Robles
Universidad de León
José M. Méndez
Universidad de Salamanca
Francisco Salto
Universidad de León

References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Selected works.Jan Łukasiewicz - 1970 - Amsterdam,: North-Holland Pub. Co.. Edited by Ludwik Borkowski.
Many-valued logics.Grzegorz Malinowski - 1993 - New York: Oxford University Press. Edited by L. Goble.

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