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More specifically, the step where the clause is negated needs to take into account the quantifiers and the variables occurring in the clause. As the negation of a universally quantified formula is an existentially quantified negated formula, the refutation proof uses ← hθ, b1 θ ←, ... , bn θ ←, where θ is a so-called skolem substitution. , bn by distinct constants not appearing anywhere else in the theory or clause. 37. 5 Prolog and SLD-resolution 35 flies(X) ← bird(X) |= flies(Y) ← bird(Y), normal(Y), we need to negate the clause.
If the query is posed a number of times, it is useful to define a new predicate cites/2 using the clause: cites(A, B) ← authorOf(A, P), reference(P, Q), authorOf(B, Q) This clause states that A cites B if A is the authorOf P, P references Q, and B is the authorOf Q. This clause corresponds to the definition of a view or an intensional relation in relational database terminology, which can be implemented by the following statement in SQL. Pub2 1 The reader unfamiliar with SQL can safely skip the SQL queries.
Unification is needed to make a literal in one clause match a literal in the other clause. For instance, when trying to resolve father(X, Y) ← parent(X, Y), male(X) with ← father(luc, maarten) it is necessary to unify the literals father(X, Y) and father(luc, maarten) using the substitution {X/luc, Y/maarten} to yield the clause ← parent(luc, maarten), male(luc). Unification was already implicitly used in Algos. 2. Formally, a unifier of two expressions f1 and f2 (terms or atoms) is a substitution such that f1 θ = f2 θ.