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Show 38 Example: Let C1 = {P(f(a,x)), Q(x)} and C2 = {f(y,c) = g(y), Q(a)}. Paramodulation of C2 into f(a ,x) in C1 yields {P(g(a)), Q( c), Q(a)}. Paramodulation of c2 into the first X in c, infers {P(f(a,g(y))), Q(g(y)), Q(a)}. D To some extent, Algorithm 3 can be viewed as a variant of paramodulation when restricted to unit equality clauses, i.e., when all atomic formulas are equality predicates. In paramodulation, a set of functionally reflexive axioms is needed, i.e., for all n-ary function symbols occurring in the sentence. Using axioms in SFR' terms can be constructed by paramodulation into variables. The term construe-tion process described in this chapter has some similarities with paramodulation into variables, while narrowing is a goal oriented version* of paramodulation into nonvariable terms. It is shown in [80] that paramodulation into variables and the set of functionally reflexive axioms are needed when the set- of-support strategy (goal oriented strategies are special cases of the set-of-support strategy) is used. Narrowing is essentially a restricted form of paramodulation. The dif-ferences are: * 1. Paramodulation allows substitution of terms into variables, while narrowing replaces terms into nonvariables terms. 2. Paramodulation does not necessarily yield a goal oriented procedure, while narrowing is a goal oriented procedure. A goal oriented deduction is a sequence of goals, each one being a derived goal of its predecessor by one step deduction. This is also called linear deduction. |
