2012/08/14 by Wojciech Dzik, Dzik, Wojciech, Jouni Järvinen +3
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1208.2971
openalex publication_date 2012/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Earlier, the authors introduced the logic IntGC, which is an extension of intuitionistic propositional logic by two rules of inference mimicking the performance of Galois connections (Logic J. of the IGPL, 18:837-858, 2010). In this paper, the extensions Int2GC and Int2GC+FS of IntGC are studied. Int2GC can be seen as a fusion of two IntGC logics, and Int2GC+FS is obtained from Int2GC by adding instances of duality-like connections \Diamond(A → B) → (\Box A → \Diamond B) and (\Diamond A → \Box B) → \Box(A → B), introduced by G. Fischer Servi (Rend. Sem. Mat. Univers. Politecn. Torino, 42:179-194, 1984), for interlinking the two Galois connections of Int2GC. Both Kripke-style and algebraic semantics are presented for Int2GC and Int2GC+FS, and the logics are proved to be complete with respect to both of these semantics. We show that rough lattice-valued fuzzy sets defined on complete Heyting algebras are proper algebraic models for Int2GC+FS. We also prove that Int2GC+FS is equivalent to the intuitionistic tense logic IKt, and an axiomatisation of IKt with the number of axioms reduced to the half of the number of axioms given by W. B. Ewald (J. Symb. Log, 51:166-179, 1986) is presented.