Unify Formula Resolution For Free

When programming in Prolog, we spend a lot of time thinking about how variables and rules "match" or "are assigned." There are actually two aspects to this. The first, "unification," regards how terms are matched and variables assigned to make terms match. The second, "resolution," is described in separate notes.

The way in which Prolog matches two terms is called unification. The idea is similar to that of unification in logic: we have two terms and we want to see if they can be made to represent the same structure. For example, we might have in our database the single Polog clause: parent(alan, clive).

The resolution method uses a process called unification to determine which clauses can be combined. Unification is the process of finding a substitution that makes two literals the same. For example, the literals "P" and "Q" can be unified by the substitution {P/Q}.

The most general unifier of U is a unifier ? such that any other unifier ? is an instance of ?. Martelli and Montanari's algorithm finds the most general unifier for a unification problem if a solution exists, otherwise it fails, indicating that there are no solutions.

Unification is a key concept in proofs by resolutions. Resolution is a single inference rule which can efficiently operate on the conjunctive normal form or clausal form. Clause: Disjunction of literals (an atomic sentence) is called a clause.

Most General Unifier Example: Suppose you have two expressions p(X) an p(Y). One way to unify these is to substitute any constant expression for X and Y: { fred/X, fred/Y }. But this is not the most general unifier, because if we substitute any variable for X and Y, we get a more general unifier: { Z/X, Z/Y }.

Prolog execution is based on the Resolution proof method. Resolution is a technique of producing a new clause by resolving two clauses that contain a complimentary literal and Resolution produces proof by Refutation.