Journal article

Constant domain quantified modal logics without Boolean negation

GA RESTALL

Australasian Journal of Logic | Victoria University of Wellington | Published : 2005

Abstract

This 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 twoplace modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s presentation of the completeness proof quite closely [10]), but with an important twist, to do with the absence of Boolean negation.

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