Characterising intermediate tense logics in terms of Galois connections

Por • 4 feb, 2014 • Sección: Educacion

Wojciech Dzik, Jouni Järvinen, Michiro Kondo

Abstract: We propose a uniform way of defining for every logic L  intermediate between intuitionistic and classical logics, the corresponding intermediate minimal 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 here L2GC+FS  . In the cases of intuitionistic logic Int  and classical logic Cl  , it is noted that Int2GC+FS  is syntactically equivalent to intuitionistic minimal tense logic IK t   by W. B.Ewald and Cl2GC+FS  equals classical minimal tense logic K t   . This justifies to consider L2GC+FS  as minimal L  -tense logic LK t   for any intermediate logic L  . We define H2GC+FS-algebras as expansions of HK1-algebras, introduced by E. Or{\l}owska 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.

arXiv:1401.7646v1 [math.LO]

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