Proof-Theoretic Functional Completeness for the Connexive Logic C
Sara Ayhan, Hrafn Valtýr Oddsson · Studia Logica · 2025
Abstract We show the functional completeness for the connectives of the non-trivial negation inconsistent logic by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that contains a strong negation, expressing a notion of direct refutation, the proof needs to be applied in a bilateralist way in that not only higher-order rule schemata for proofs but also for refutations need to be considered. Secondly, given that is a connexive logic we need to take a connexive understanding of inference as a basis, leading to a different conception of (higher-order) refutation than is usually employed.