Routely-Meyer Semantics for some weak Boolean Logics, and some Translations
E. Yang · Logic Journal of IGPL · 2004
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