First-order proofs without syntax
Dominic Hughes ( Chief Scientist, concept.io )
Proofs of first-order logic are traditionally syntactic, built inductively from symbolic inference rules. This talk reformulates first-order logic with proofs which are combinatorial rather than syntactic. A combinatorial proof is defined by graph-theoretic conditions, verifiable in polynomial time.
To be accessible to a broad audience of computer scientists, mathematicians and logicians, this lecture uses many illustrative examples and presupposes only introductory undergraduate-level logic.
This work extends 'Proofs Without Syntax' [Annals of Mathematics, 2006], which treated the propositional case.