Constant Domain Quantified Modal Logics Without Boolean Negation

Authors

  • Greg Restall Philosophy Department, University of Melbourne

DOI:

https://doi.org/10.26686/ajl.v3i0.1772

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.

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Author Biography

Greg Restall, Philosophy Department, University of Melbourne

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Published

2005-07-08