Constant domain quantified modal logics without Boolean negation
Australasian Journal of Logic | Victoria University of Wellington | Published : 2005
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 ), but with an important twist, to do with the absence of Boolean negation.