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

Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities