Constant Domain Quantified Modal Logics Without Boolean Negation

  • Greg Restall Philosophy Department, University of Melbourne

Abstract

his paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a two-place modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s 1984 presentation of the completeness proof quite closely), but with an important twist, to do with the absence of Boolean negation.

Author Biography

Greg Restall, Philosophy Department, University of Melbourne
Published
2005-07-08
How to Cite
RESTALL, Greg. Constant Domain Quantified Modal Logics Without Boolean Negation. The Australasian Journal of Logic, [S.l.], v. 3, july 2005. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1772>. Date accessed: 23 nov. 2019. doi: https://doi.org/10.26686/ajl.v3i0.1772.