Resumen de Dual equivalent two-valued under-determined and over-determined Interpretations for ukasiewicz's 3-valued Logic 3
Gemma Robles Vázquez, Francisco Salto Alemany, José M. Méndez
ukasiewicz three-valued logic 3 is often understood as the set of all 3-valued valid formulas according to ukasiewicz's 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of 3: "well-determined" 3a and "truth-preserving" 3b 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 3, 3a and 3b. The logic 3 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" ukasiewicz logics are paraconsistent
