Polyadic Algebras over Nonclassical Logics
نویسندگان
چکیده
The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc. Introduction. In [19] H. Rasiowa identifies a large class of propositional logics, the standard implicational calculi (SIC’s), that can be algebraized in a meaningful way and which include most of the nonclassical logics considered in the literature: classical and intuitionistic logic and their various weakenings and fragments, the multiple-valued logics of Post and Lukasiewicz, the modal logics that admit the rule of necessitation, BCK logic, etc. The main purpose of this 1991 Mathematics Subject Classification: Primary 03G15; Secondary 03B22, 03B40, 08A05.
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