Clause

A clause is a logical rule in a logic program. Formally, a clause is a disjunction of (possibly negated) literals, such as

$$\displaystyle\begin{array}{rcl} \mathit{grandfather}(x,y)& \vee & \neg \mathit{father}(x,z) {}\\ & \vee & \neg \mathit{parent}(z,y) {}\\ \end{array}$$

In the logic programming language Prolog this clause is written as

grandfather(X,Y) :- father(X,Z),                     parent(Z,Y).

The part to the left of :- (“if”) is the head of the clause, and the right part is its body. Informally, the clause asserts the truth of the head given the truth of the body. A clause with exactly one literal in the head is called a Horn clause or definite clause; logic programs mostly consist of definite clauses. A clause without a body is also called a fact; a clause without a head is also called a denial, or a query in a proof by refutation. The clause without head or body is called the empty clause: it signifies inconsistency or falsehood and is denoted □. Given a set of clauses, the resolution...