Unification (computer Science) - Definition of Unification For First-order Logic

Definition of Unification For First-order Logic

Let p and q be sentences in first-order logic.

UNIFY(p,q) = U where subst(U,p) = subst(U,q)

Where subst(U,p) means the result of applying substitution U on the sentence p. Then U is called a unifier for p and q. The unification of p and q is the result of applying U to both of them.

Let L be a set of sentences, for example, L = {p,q}. A unifier U is called a most general unifier for L if, for all unifiers U' of L, there exists a substitution s such that applying s to the result of applying U to L gives the same result as applying U' to L:

subst(U',L) = subst(s,subst(U,L)).

Read more about this topic:  Unification (computer Science)

Famous quotes containing the words definition of, definition and/or logic:

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)

    Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?
    Richard Eberhart (b. 1904)

    The much vaunted male logic isn’t logical, because they display prejudices—against half the human race—that are considered prejudices according to any dictionary definition.
    Eva Figes (b. 1932)