Minimal p-morphic Images, Axiomatizations and Coverings in the Modal Logic K4

We define the concepts of minimal p-morphic image and basic p-morphism for transitive Kripke frames. These concepts are used to determine effectively the least number of variables necessary to axiomatize a tabular extension of K4, and to describe the covers and co-covers of such a logic in the lattice of the extensions of K4.

[1]  Marcus Kracht,et al.  Splittings and the finite model property , 1991, Journal of Symbolic Logic.

[2]  W. J. Blok,et al.  Pretabular varieties of modal algebras , 1980 .

[3]  Kit Fine,et al.  Logics containing K4. Part I , 1974, Journal of Symbolic Logic.

[4]  Marcus Kracht,et al.  An almost general splitting theorem for modal logic , 1990, Stud Logica.

[5]  Fabio Bellissima,et al.  Post Complete and 0-Axiomatizable Modal Logics , 1990, Ann. Pure Appl. Log..

[6]  W. Blok.  Varieties of interior algebras , 1976 .

[7]  Wolfgang Rautenberg,et al.  Splitting lattices of logics , 1980, Arch. Math. Log..

[8]  Willem J. Blok,et al.  The lattice of modal logics: an algebraic investigation , 1980, Journal of Symbolic Logic.

[9]  Saverio Cittadini,et al.  Minimal Axiomatization in Modal Logic , 1997, Math. Log. Q..