Abstract : Solving goals---like deciding word problems or resolving constraints---is much easier in some theory presentations than in others. What have been called ``completion processes'', in particular in the study of equational logic, involve finding appropriate presentations of a given theory to solve easily a given class of problems. We provide a general proof-theoretic setting within which completion-like processes can be modelled and studied. This framework centers around well-founded orderings of proofs. It allows for abstract definitions and very general characterizations of saturation processes and redundancy criteria.
https://hal.inria.fr/inria-00099466
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Nachum Dershowitz, Claude Kirchner. Abstract Saturation-based Inference. Eighteenth Annual IEEE Symposium on Logic in Computer Science - LICS'2003), Jun 2003, Ottawa, Canada, 10 p. ⟨inria-00099466⟩
