Publication Date:
2014-11-21
Description:
We propose a uniform way of defining for every logic L intermediate between intuitionistic and classical logics, the corresponding intermediate tense logic LK t . This is done by building the fusion of two copies of intermediate logic with a Galois connection LGC , and then interlinking their operators by two Fischer Servi axioms. The resulting system is called L2GC + FS . In the cases of intuitionistic logic Int and classical logic Cl , it is noted that Int2GC + FS is syntactically equivalent to intuitionistic tense logic IK t by W. B. Ewald and Cl2GC + FS equals classical tense logic K t . This justifies calling L2GC + FS the L -tense logic LK t for any intermediate logic L . We define H2GC + FS-algebras as expansions of HK1-algebras, introduced by E. Orłowska and I. Rewitzky. For each intermediate logic L , we show algebraic completeness of L2GC + FS and its conservativeness over L . We prove relational completeness of Int2GC + FS with respect to the models defined on IK -frames introduced by G. Fischer Servi. We also prove a representation theorem stating that every H2GC + FS-algebra can be embedded into the complex algebra of its canonical IK -frame.
Print ISSN:
1367-0751
Electronic ISSN:
1368-9894
Topics:
Mathematics
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