TY - JOUR
T1 - Abstract canonical presentations
AU - Dershowitz, Nachum
AU - Kirchner, Claude
N1 - Funding Information:
This paper is a revised and extended version of one presented in 2002 by the first author at the Clifford Lectures in Mathematical Logic for Computer Science at Tulane University and by the second author at the UNIF workshop [18], and which appeared in the Proceedings of the Symposium on Logic in Computer Science [19]. ∗Corresponding author. E-mail addresses: Nachum.Dershowitz@cs.tau.ac.il (N. Dershowitz), Claude.Kirchner@loria.fr (C. Kirchner). 1Supported in part by the Israel Science Foundation (Grant no. 250/05).
PY - 2006/7/25
Y1 - 2006/7/25
N2 - Solving goals-like proving properties, deciding word problems or resolving constraints-is much easier with some presentations of the underlying theory than with others. Typically, what have been called "completion processes", in particular in the study of equational logic, involve finding appropriate presentations of a given theory to more easily solve a given class of problems. We provide a general proof-theoretic setting that relies directly on the fundamental concept of "good", that is, normal-form, proofs, itself defined using well-founded orderings on proof objects. This foundational framework allows for abstract definitions of canonical presentations and very general characterizations of saturation and redundancy criteria.
AB - Solving goals-like proving properties, deciding word problems or resolving constraints-is much easier with some presentations of the underlying theory than with others. Typically, what have been called "completion processes", in particular in the study of equational logic, involve finding appropriate presentations of a given theory to more easily solve a given class of problems. We provide a general proof-theoretic setting that relies directly on the fundamental concept of "good", that is, normal-form, proofs, itself defined using well-founded orderings on proof objects. This foundational framework allows for abstract definitions of canonical presentations and very general characterizations of saturation and redundancy criteria.
KW - Canonical rewriting
KW - Canonicity
KW - Completion
KW - Proof orderings
KW - Redundancy
KW - Saturation
UR - http://www.scopus.com/inward/record.url?scp=33745656625&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2006.03.012
DO - 10.1016/j.tcs.2006.03.012
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AN - SCOPUS:33745656625
SN - 0304-3975
VL - 357
SP - 53
EP - 69
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 1-3
ER -