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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“What avail all your scholarly accomplishments and learning, compared with wisdom and manhood? To omit his other behavior, see what a work this comparatively unread and unlettered man wrote within six weeks. Where is our professor of belles-lettres, or of logic and rhetoric, who can write so well?”
—Henry David Thoreau (1817–1862)