Routely-Meyer Semantics for some weak Boolean Logics, and some Translations

Author: Eunsuk Yang

Source: Logic Journal of the IGPL, Volume 12, Number 5, September 2004 , pp. 355-369(15)

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Abstract:

In this paper we investigate some logics with weak Boolean (wB) negation (-), calling wB logics, obtained by dualizing intuitionistic negation (¬). We first provide Routley-Meyer (RM) semantics for wB-IC (the intuitionistic propositional logic IC with - in place of ¬), its neighbors wB-LC, wB-LC^* (the extensions of wB-IC with the chain (c)), and wB-S4, wB-S4c (the systems with the strict implication as well as -). We give completeness for each of them by using RM semantics. We next provide RM semantics for IC, the Dummett's LC, the wB-S4 with ¬ in place of - (pB-S4), and the pB-S4 with c (pB-S4c), and give completeness for each system. Finally, we give a translation of the classical propositional logic PC into wB-IC, and a translation of PC into wB-S4c.¹

Keywords: Weak Boolean negation and logics; wB-IC; wB-LC; wB-S4; Routley-Meyer semantics

Document Type: Research article

Publication date: 2004-09-01

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Logic Journal of the IGPL publishes papers in all areas of pure and applied logic, including pure logical systems, proof theory, model theory, recursion theory, type theory, nonclassical logics, nonmonotonic logic, numerical and uncertainty reasoning, logic and AI, foundations of logic programming, logic and computation, logic and language, and logic engineering.