Boolean logics with relations

The language of our Boolean logic with relations is a Boolean language to which relation symbols have been added. Such a language turns out to be a useful tool for describing relational structures and algebraic structures. This paper introduces the concepts of Kripke semantics and Boolean semantics for our language. It addresses the traditional issues of decidability/complexity and axiomatization/completeness but it also defines the new concepts of weak canonicity and strong canonicity.