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<p>We show the functional completeness for the connectives of the non-trivial negation inconsistent logic <Emphasis FontCategory="NonProportional">C</Emphasis> by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that <Emphasis FontCategory="NonProportional">C</Emphasis> 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 <Emphasis FontCategory="NonProportional">C</Emphasis> 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.</p>

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Proof-Theoretic Functional Completeness for the Connexive Logic C

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  • 发表日期：

    2025年7月8日

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  • Sara Ayhan,
  • Hrafn Valtýr Oddsson

摘要

We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C 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 C 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.