Abstract
This paper is devoted to showing certain connections between normal modal logics and those strictly regular modal logics which have □ ⊤ → □□ ⊤ as a theorem. We extend some results of E. J. Lemmon (cf. [66]). In particular we prove that the lattice of the strictly regular modal logics with the axiom □ ⊤ → □□ ⊤ is isomorphic to the lattice of the normal modal logics.
Similar content being viewed by others
References
E. J. Lemmon,Algebraic semantics for modal logics I, II,Journal of Symbolic Logic 33 (1966), pp. 46–65 and 191–218.
Author information
Authors and Affiliations
Additional information
The results in this paper were reported at Logic Colloquium '87 in Granada.
Rights and permissions
About this article
Cite this article
Świrydowicz, K. On regular modal logics with axiom □ ⊤ → □□ ⊤. Stud Logica 49, 171–174 (1990). https://doi.org/10.1007/BF00935596
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00935596