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)
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