© 2004 by Oxford University Press
Routely-Meyer Semantics for some weak Boolean Logics, and some Translations
Institute of Yonsei Philosophy, Yonsei University, Rm 523 College of Liberal Arts, Seodaemun, Seoul, 120-789, KOREA. E-mail: yanges2{at}hanmail.net
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
Key Words: Weak Boolean negation and logics, wB-IC, wB-LC, wB-S4, Routley-Meyer semantics
Received 25 May 2002. Revised 5 August 2004.
1This work was supported by the Korea Research Foundation Grant KRF-2000-037-BB0012. It was also partially supported by the School of Informatics Grant. I thank the School of Informatics at Indiana University. I am also indebted to Professor J. M. Dunn, who was my advisor during my research visit at Indiana University, for helpful advice and guidance concerning the persent paper.