By Buchberger B., Campbell J. A. (Ed)
This publication constitutes the refereed lawsuits of the seventh foreign convention on synthetic Intelligence and Symbolic Computation, AISC 2004, held in Linz, Austria in September 2004.The 17 revised complete papers and four revised brief papers provided including four invited papers have been conscientiously reviewed and chosen for inclusion within the publication. The papers are dedicated to all present features within the zone of symbolic computing and AI: mathematical foundations, implementations, and purposes in and academia.
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Extra info for Artificial Intelligence and Symbolic Computation: 7th International Conference, AISC 2004, Linz, Austria, September 22-24, 2004, Proceedings
Wave-rule’ can be defined formally. It is a rewrite rule containing wave annotation in which the skeletons are preserved and the wave-front measure of the right-hand side is less than that of the left-hand side. Informally, the skeleton consists of those bits of the expression outside of wave-fronts or inside the wave-holes. The measure records the position of the wave-fronts in the skeleton. It decreases when outwards directed wave-fronts move out or downwards wave-fronts move in. A formal definition of skeleton and of the wave-front measure can be found in [Basin & Walsh, 1996] and in chapter 4 of [Bundy et al, 2005].
Hence, for by the argument in the previous case, and similarly Since arbitrary) by assumption, and only affects and we obtain as required. can now be proved as in the previous case. Case flex-rigid, is Subcase occurrence check: contains (a critical subterm with head) Then clearly there is no Q-substitution such that Subcase pruning: Here contains a subterm with in Q, and free in Then is Q with replaced by and 1. , and for We must show that is a For We need to show But For and follows from We need to show But since coincide on all variables free in is a new variable, and the claim Proof Search in Minimal Logic 2.
Annotations in the goal mark those subexpressions which correspond to bits of the given (the skeleton) and those which do not (the wave-fronts). e. rewriting can only move the wave-fronts around within the skeleton - wave-fronts can change but the skeleton cannot. Furthermore, wave-fronts are given a direction (outwards or inwards) and movement can only be in that direction. Outward wave-fronts can mutate to inward, but not vice versa. This ensures termination. Rippling can be implemented by putting wave annotation into the rewrite rules to turn them into wave-rules, see Fig.
Artificial Intelligence and Symbolic Computation: 7th International Conference, AISC 2004, Linz, Austria, September 22-24, 2004, Proceedings by Buchberger B., Campbell J. A. (Ed)