A structural completeness theorem for a class of conditional rewrite rule systems
For a class of quantifier-free logical theories, axiomatized by conditional equivalences, we prove a completeness result of the form: if a theory T from the class generates the uniquely terminating conditional rewrite rule system, and a partition T1 ∪ T2 of T satisfies certain structural properties, then an arbitrary unquantified formula Ω is a theorem of T1 ∪ T2 iff the leaves of any proof tree for Ω are theorems of T1.
Key words and phrasesconditional rewrite rules inference rules proof search reduction case splitting strong completeness confluency finite termination decision algorithms
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