By Buchberger B., Campbell J. A. (Ed)

ISBN-10: 3540302107

ISBN-13: 9783540302100

This booklet constitutes the refereed court cases 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 awarded including four invited papers have been conscientiously reviewed and chosen for inclusion within the booklet. The papers are dedicated to all present facets within the zone of symbolic computing and AI: mathematical foundations, implementations, and purposes in and academia.

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**Sample text**

We have the following standard abbreviations: The universal quantification will be introduced later (as a kind of generalized conjunction). A suitable abbreviation for is also provided later. As explained we have an infinite number of truth values (truth codes) in general, but the special cases of three-valued and four-valued logics are interesting too. In order to investigate finite truth tables we first add just as an indeterminacy. We do not have Unfortunately we do have that entails (try with and using the truth tables and use the fact that any entails itself).

This enabled the idea to be considerably generalized. Later we 32 A. Bundy invented ‘rippling-sideways’, ‘rippling-in’, etc and so generalized the combined technique to ‘rippling’. 2 Relation to Standard Rewriting Techniques Are Wave-Rules Just the Step Cases of Recursive Definitions? No. Many lemmas and other axioms can also be annotated as wave-rules. Examples include: associative laws; distributive laws; replacement axioms for equality; many logical axioms; etc. Equations that cannot be expressed as wave-rules include commutative laws and (usually) the step cases from mutually recursive definitions.

Corollary 2. , a unification problem 22 H. Schwichtenberg with no unification pairs) such that for any is an and every can be obtained in this way. Since the empty substitution is a is an which is most general in the sense stated. denotes the result of the unification algorithm at 4 Proof Search A Q-sequent has the form where is a list of Q-clauses and G is a Q-goal. We write to indicate that all assumption variables in the derivation M concern clauses in Write S for a set S of sequents if there are derivations in long normal form for all such that Let S mean We now prove correctness and completeness of the proof search procedure: correctness is the if-part of the two lemmata to follow, and completeness the only-if-part.

### Artificial Intelligence and Symbolic Computation: 7th International Conference, AISC 2004, Linz, Austria, September 22-24, 2004, Proceedings by Buchberger B., Campbell J. A. (Ed)

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