An Algebraic Investigation of the Connexive Logic C

In this paper we show that axiomatic extensions of H. Wansing's connexive logic C (C-?) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of C(C-?)-algebras. We develop the structure theory of C(C-?)-algebras, and we prove their representability in terms of twist-like constructions over implicative lattices (Heyting algebras). As a consequence, we further clarify the relationship between the aforementioned classes. Finally, taking advantage of the above machinery, we provide some preliminary remarks on the lattice of axiomatic extensions of C (C-?) as well as on some properties of their equivalent algebraic semantics.