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arXiv · 1906.11236

First-order proofs without syntax

Dominic J. D. Hughes
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Abstract

Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula $\phi$ as a lax fibration over a graph associated with $\phi$. The main theorem is soundness and completeness: a formula is a valid if and only if it has a combinatorial proof.

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Dominic J. D. Hughes. 2019-06-26. First-order proofs without syntax. https://arxiv.org/abs/1906.11236

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