The McKinsey–Lemmon logic is barely canonical

  • Robert Goldblatt Centre for Logic, Language and Computation, Victoria University of Wellington
  • Ian Hodkinson Department of Computing, Imperial College London

Abstract

We study a canonical modal logic introduced by Lemmon, and axiomatised by an infinite sequence of axioms generalising McKinsey’s formula. We prove that the class of all frames for this logic is not closed under elementary equivalence, and so is non-elementary. We also show that any axiomatisation of the logic involves infinitely many non-canonical formulas.

Author Biographies

Robert Goldblatt, Centre for Logic, Language and Computation, Victoria University of Wellington
Ian Hodkinson, Department of Computing, Imperial College London
Published
2007-11-06
How to Cite
GOLDBLATT, Robert; HODKINSON, Ian. The McKinsey–Lemmon logic is barely canonical. The Australasian Journal of Logic, [S.l.], v. 5, nov. 2007. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1783>. Date accessed: 21 sep. 2019. doi: https://doi.org/10.26686/ajl.v5i0.1783.