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)

Publisher: Oxford University Press

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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

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