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arXiv · 2304.05085

Complementation: a bridge between finite and infinite proofs

Gilles Dowek·Ying Jiang
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Abstract

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof in a different inference system. In this paper, we show that, for some decidable inference systems, this (possibly) infinite proof has a representation as a finite proof in yet another system, equivalent to the previous one.

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Gilles Dowek, Ying Jiang. 2023-04-11. Complementation: a bridge between finite and infinite proofs. https://arxiv.org/abs/2304.05085

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