Well-Foundedness Is Sufficient for Completeness of Ordered Paramodulation
For many years all known completeness results for Knuth-Bendix completion and ordered paramodulation required the term ordering ≻ to be well-founded, monotonic and total(izable) on ground terms. Then, it was shown that well-foundedness and the subterm property were enough for ensuring completeness of ordered paramodulation.
Here we show that the subterm property is not necessary either. By using a new restricted form of rewriting we obtain a completeness proof of ordered paramodulation for Horn clauses with equality where well-foundedness of the ordering suffices. Apart from the fundamental interest of this result, some potential applications motivating the interest of dropping the subterm property are given.
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