First-order proofs without syntax
arXiv:1906.11236
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 as a lax fibration over a graph associated with . The main theorem is soundness and completeness: a formula is a valid if and only if it has a combinatorial proof.
42 pages