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A substitution, $\sigma$ , is a most general unifier (mgu) of a set of expressions $E$ if it unifies $E$ , and for any unifier, $\omega$ ...

θ = {a/x,f (b)/y} is a (most general) unifier for the set. Page 19. Substitution and. Uni cation. An algorithm for Uni cation.

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Nov 10, 2015 · You can compute most general unifiers by taking formulas pairwise and lining them up to help you to compute most general unifiers for the pairs. Thus, z/g (x) yields P (g (x), g (c)) and P (g (x), g (x)). Consequently, z/g (x), x/c which becomes {z/g (c), x/c} indicates the most general unifier of those two wffs.

17.12.2021 · A unifier for the set of expressions is called the most general unifier if, for any other unifier for the same set of expressions , there is yet another unifier such that . A unification algorithm takes a set of expressions as its input. If this set is not unifiable, the algorithm terminates and yields a negative result.

Resolution Up: Notes 7/2/2001 Previous: Unifiers Most General Unifier. A substitution, , is a most general unifier (mgu) of a set of expressions if it unifies , and for any unifier, , of , there is a unifier, , such that . The idea is that is less specific than (technically, no more specific than) , that is, we can substitute for some of the variables of and get .

Hope this kind of tough example helps some of you get the hang of this algorithm :)

Most General Unifier. A substitution, , is a most general unifier (mgu) of a set of expressions if it unifies , and for any unifier, , of , there is a unifier, , such that . The idea is that is less specific than (technically, no more specific than) , that is, we can substitute for some of the variables of and get . Note that there can be more ...

If there exists a unifier for the input set of expressions, the algorithm yields the most general unifier for this set of expressions. The unification algorithm ...

This program allows you select two terms, in prefix form, and find their most general unifier, if it exists. (See Sec. 3.12.2 and Sec. 4.7.2 of LMCS). You can Find the Critical Pairs for two Term Rewrite Rules s 1--> t 1 and s 2--> t 2.

A unifier of two terms t and t ' is a substitution function ϕ that maps variables to terms such that ϕ t = ϕ t ′, i.e., applying ϕ to the variables in each term yields the same term. For example, given t = f ( x) and t ′ = f ( a) where a is a constant and f is a function name (not a variable) then ϕ x ↦ a is a unifier since ϕ t = f ...

10.11.2015 · You can compute most general unifiers by taking formulas pairwise and lining them up to help you to compute most general unifiers for the pairs. Thus, z/g (x) yields P (g (x), g (c)) and P (g (x), g (x)). Consequently, z/g (x), x/c which becomes {z/g (c), x/c} indicates the most general unifier of those two wffs.

This program allows you to input a term or atomic formula in prefix form and have it ... in prefix form, and find their most general unifier, if it exists.

The substitution variables are called Most General Unifier or MGU. E.g. Let's say there are two different expressions, P(x, y), and P(a, f(z)).

Numerous decision pro- cedures for formula satisfiability modulo equational theories also rely on unification, either based on narrowing [36] or by using ...

Hope this kind of tough example helps some of you get the hang of this algorithm :)

The simple algorithm that is used in practice (e.g. in Prolog) is exponential for pathological cases. There is a theoretically more ...

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To make the second coordinates match one can set z=f(u,v),y=f(a,b). With this value of z matched to the other first coordinate z=f(x,g(x,y)) a choice ...

This program allows you select two terms, in prefix form, and find their most general unifier, if it exists. (See Sec. 3.12.2 and Sec. 4.7.2 of LMCS).

Slide 9 of 13

Dec 17, 2021 · A unifier for the set of expressions is called the most general unifier if, for any other unifier for the same set of expressions , there is yet another unifier such that . A unification algorithm takes a set of expressions as its input. If this set is not unifiable, the algorithm terminates and yields a negative result.