Completeness proofs via canonical models on increasingly generalized settings
Maurice Pico

Abstract:
In the present thesis we will expand Restall's completeness proof and
present it on a wider context. He proposes an adaption of the
completeness proof for constant domains predicate modal logic to the
wider case of a distributive setting expanded with unary modal
operators and enriched with constant domain quantification. The
overall motivation stems from the pending problem of finding a clearer
semantics for quantified relevance logics. First, unlike Restall's
paper, soundness and the truth lemma are explicitly proved, in fact
the overall proof is presented in a more clarified and structured way,
in line with classic literature on modal completeness. Moreover, a
flaw in the original proof is repaired.

Keywords: Logic;  Mathematics