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- Title
Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz's 3-valued Logic Ł3.
- Authors
Robles, Gemma; Salto, Francisco; Méndez, José
- 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.
- Subjects
TERNARY logic; HERMENEUTICS; EQUIVALENCE (Linguistics); SEMANTICS; LINGUISTIC analysis
- Publication
Journal of Philosophical Logic, 2014, Vol 43, Issue 2/3, p303
- ISSN
0022-3611
- Publication type
Article
- DOI
10.1007/s10992-012-9264-0