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:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“Though living is a dreadful thing
And a dreadful thing is it
Life the niggard will not thank,
She will not teach who will not sing,
And what serves, on the final bank,
Our logic and our wit?”
—Philip Larkin (1922–1986)