Inspired by the efficient proof procedures discussed in Computability logic [3],[5],[6], we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system [2] 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.

Conceptual graph formalism is a knowledge representation language in AI based on a graphical form of logic. Although logic is the basis of the conceptual graph theory, there is a strongly felt absence of a formal treatment of conceptual graphs as a logic programming language. In this paper, we develop the notion of a conceptual graph program as a kind of graph-based order-sorted logic program. First, we define the syntax of the conceptual graph program by specifying its major syntactic elements. Then, we develop a kind of model theoretic semantics and fixpoint semantics of the conceptual graph program. Finally, we show that the two types of semantics coincide for the conceptual graph programs.