A Heuristic Proof Procedure for First-Order Logic
Abstract
Inspired by the efficient proof procedures discussed in Computability logic Jap03,Japic,Japfin, we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system and has the following features: (a)~ it views sequents as games between the machine and the environment, and (b)~ it views proofs as a winning strategy of the machine. From this game-based viewpoint, a poweful heuristic can be extracted and a fair degree of determinism in proof search can be obtained. This article proposes a new deductive system LKg with respect to first-order logic and proves its soundness and completeness. We also discuss LKg', a variant of LKg with some optimizations added.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.