In this paper we show that axiomatic extensions of H. Wansing’s connexive logic \(\textsf{C}\) (\(\textsf{C}^{\perp }\)) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of \(\textsf{C}\)(\(\textsf{C}^{\perp }\))-algebras. We develop the structure theory of \(\textsf{C}\)(\(\textsf{C}^{\perp }\))-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 \(\textsf{C}\) (\(\textsf{C}^{\perp }\)) as well as on some properties of their equivalent algebraic semantics.

在本文中，我们证明 H. Wansing 的连接逻辑\(\textsf{C}\) ( \(\textsf{C}^{\perp }\) )的公理扩展是可代数的（在 JW Blok 和 D 的意义上） . Pigozzi) 相对于\(\textsf{C}\) ( \(\textsf{C}^{\perp }\) )代数的子变种。我们发展了\(\textsf{C}\) ( \(\textsf{C}^{\perp }\) )代数的结构理论，并证明了它们在隐含格上的扭曲结构的可表示性 (海廷代数）。因此，我们进一步阐明了上述类之间的关系。最后，利用上述机制，我们对公理扩张的格提供一些初步评论\(\textsf{C}\) ( \(\textsf{C}^{\perp }\) )以及其等效代数语义的一些属性。