First-order proofs without syntax
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.
PDF AbstractCategories
Logic
Combinatorics
03B05, 05C99
F.4.1; G.2.1; G.2.2; G.2.3
