unification
unification An operation on wellformed formulas, namely that of finding a most general common instance. The formulas can be terms or atomic formulas (see predicate calculus). A common instance of two formulas A and B is a formula that is an instance of both of them, i.e. that can be obtained from either by some consistent substitution of terms for variables. As an example let A and B be the following:
A = p(f(u),v)
B = p(w,g(x))
Let u, v, w, x, y, z be variables, and c, d constants. Consider the substitution that replaces u, v, w, x respectively by the terms y, g(z), f(y), z. This substitution, when applied to A and B, transforms them both into the same formula I_{1}, where
I_{1} = P(f(y), g(z))
Hence the above is a common instance of A and B. It is however only one of infinitely many: other common instances of A and B include
I_{2} = P(f(z),g(y))
I_{3} = P(f(y),g(y))
I_{4} = P(f(f(y)),g(g(z)))
I_{5} = P(f(c),g(d))
Note that I_{2}, I_{3}, I_{4}, I_{5} are themselves instances of I_{1}. In fact any common instance of A and B is an instance of I_{1} and therefore I_{1} is called a most general common instance of A and B. Of the formulas above, the only other one that is a most general common instance is I_{2}. I_{5} would also be one if c and d were variables rather than constants; indeed the y and z of I_{1} could be any two distinct variables. In some cases A and B have no common instance; two examples of this are
A = P(f(u),v)
B = P(g(w),x)
and
A = P(f(u),u)
B = P(w,f(w))
If A and B do have a common instance however, they must have a most general one. There are algorithms (the original one being Robinson's, 1965) for deciding whether a given A and B have a common instance, and if so finding a most general one. Robinson's motivation for describing unification was its role in resolution theorem proving. Resolution was at one time associated with “general problemsolving” techniques in artificial intelligence. More recently it has provided the conceptual basis for the logic programming language Prolog. Another use of unification is in compiletime typeinference, especially for polymorphic types.
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"unification." A Dictionary of Computing. . Encyclopedia.com. 24 Oct. 2017 <http://www.encyclopedia.com>.
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unification
u·ni·fi·ca·tion / ˌyoōnəfiˈkāshən/ • n. the process of being united or made into a whole. DERIVATIVES: u·ni·fi·ca·tor·y / ˈkātərē/ adj.
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"unification." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 24 Oct. 2017 <http://www.encyclopedia.com>.
"unification." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (October 24, 2017). http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/unification
"unification." The Oxford Pocket Dictionary of Current English. . Retrieved October 24, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/unification