Two results in term rewriting theorem proving
Two results are presented in this paper. (1) We extend the term rewriting approach to first order theorem proving, as described in [HsD83], to the theory of first order predicate calculus with equality. Consequently, we have showed that the term rewriting method can be as powerful as paramodulation and resolution combined. Possible improvements of efficiency are also discussed.
(2) In [KaN84], Kapur & Narendran proposed a method similar to [HsD83]. Motivated by the Kapur-Narendran method, we introduce a notion of splitting for theorem proving in first order predicate calculus. The splitting strategy provides a better utilization of the reduction mechanism of term rewriting systems than the N-strategy in [HsD83], although it generates more critical pairs. Comparisons and the relation between the splitting strategy, Kapur-Narendran method, and the N-strategy are also given.
We conjecture that our way of dealing with first order theories with full equality can be extended to the splitting and the Kapur-Narendran methods as well.
Due to the lack of space, we only give a sketch of the proofs of the completeness of the two theorem proving methods. They will be provided in detail in a longer version of the paper.
KeywordsTheorem Prove Atomic Formula Failure Node Predicate Symbol Critical Pair
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