Abstract
A language of equational programs together with an inference system, based on paramodulation is defined. The semantics of the language is given with respect to least models, least fixpoints and success sets and its soundness and completeness is proven using fixpoint theory. The necessity of the functional reflexive axioms is investigated in detail. Finally, the application of these ideas to term rewriting systems is outlined by discussing directed paramodulation and narrowing.
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Furbach, U., Hölldobler, S. & Schreiber, J. Horn equational theories and paramodulation. J Autom Reasoning 5, 309–337 (1989). https://doi.org/10.1007/BF00248322
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DOI: https://doi.org/10.1007/BF00248322