Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E

Lidia Typańska-Czajka

doi:10.18778/0138-0680.48.1.03

Authors

Lidia Typańska-Czajka Collegium Da Vinci, Poznań, Poland Author

DOI:

https://doi.org/10.18778/0138-0680.48.1.03

Keywords:

relevant logic, non-classical logics, lattice, universal algebra

Abstract

The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].

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