Unified Gentzen Approach to Connexive Logics over Wansing's C

Gentzen-style sequent calculi and Gentzen-style natural deduction systems are introduced for a family (C-family) of connexive logics over Wansing's basic connexive logic C. The C-family is derived from C by incorporating the Peirce law, the law of excluded middle, and the generalized law of excluded middle.Theorems establishing equivalence between the proposed sequent calculi and natural deduction systems are demonstrated.Cut-elimination and normalization theorems are established for the proposed sequent calculi and natural deduction systems, respectively.