Computer Science > Logic in Computer Science
[Submitted on 31 Dec 2024
]
Title: Unified Gentzen Approach to Connexive Logics over Wansing's C
Title: 统一的根岑方法在瓦辛的C上的连通逻辑
Abstract: 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.
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