Logic Programming

Abstract

Most axioms are expressed in the form: If premise-1 and premise-2 and …then conclusion. Formally, this is:

$$A = \forall {x_1} \cdots \forall {x_k}({B_1} \wedge \cdots \wedge {B_m} \to B),$$

where B and Bi are atoms. In the degenerate case where there are no antecedents, $A = \forall {x_1} \cdots \forall {x_k}B.$ In clausal form, an axiom is $\neg {B_1} \vee \cdots \vee \neg {B_m} \vee B.$ To prove that a formula $G = {G_1} \wedge \cdots \wedge {G_1}$ is a logical consequence of a set of axioms, we append $\neg G$ to the set of axioms and try to construct a refutation by resolution. $\neg G$ is called the goal clause.