Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities

Abstract

In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining one is an extension of Modal Boolean Connexive Logic with a property of closure under the function of demodalization. In our work we provide a formal presentation of mentioned properties and axiom schemata that allow us to incorporate them into the axiomatic systems. The presented axiom systems are provided with proofs of soundness and completeness. The properties of closure under negation and demodalization are motivated by the syncategorematic view on the connective of negation and modalities, which is discussed in the paper.