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On regular modal logics with axiom □ ⊤ → □□ ⊤


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.

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  1. [66]

    E. J. Lemmon,Algebraic semantics for modal logics I, II,Journal of Symbolic Logic 33 (1966), pp. 46–65 and 191–218.

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The results in this paper were reported at Logic Colloquium '87 in Granada.

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Świrydowicz, K. On regular modal logics with axiom □ ⊤ → □□ ⊤. Stud Logica 49, 171–174 (1990).

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  • Mathematical Logic
  • Modal Logic
  • Computational Linguistic
  • Normal Modal Logic
  • Regular Modal Logic