English

First-order proofs without syntax

Logic 2019-06-27 v1 Combinatorics

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 ϕ\phi as a lax fibration over a graph associated with ϕ\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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Cite

@article{arxiv.1906.11236,
  title  = {First-order proofs without syntax},
  author = {Dominic J. D. Hughes},
  journal= {arXiv preprint arXiv:1906.11236},
  year   = {2019}
}

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42 pages