Abstract:This paper presents Rasiowa-Sikorski deduction systems (R-S systems) for logics CPL, CLuN, CLuNs and mbC. For each of the logics two systems are developed: an R-S system that can be supplemented with admissible cut rule, and a KE-version of R-S system in which the non-admissible rule of cut is the only branching rule. The systems are presented in a Smullyan-like uniform notation, extended and adjusted to the aims of this paper. Completeness is proved by the use of abstract refutability properties which are dua… Show more
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