Abstract Canonical Inference

An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) "fairness," which yields completeness, and "uniform fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi

Abstract Canonical Inference Systems

Colloque sur invitation. internationale.International audienceWe provide a general proof theoretical setting under which the so-called ``completion processes'' (as used for equational reasoning) can be modeled, understood, studied, proved and generalized. This framework---based on a well-founded ordering on proofs---allows us to derive saturation processes and redundancy criteria abstractly

Automated deduction with built-in theories: completeness results and constraint solving techniques

Postprint (published version