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Mon, 03 Apr 2000 00:00:00 +0200Mon, 03 Apr 2000 00:00:00 +0200Canonical Conditional Rewrite Systems Containing Extra Variables
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/344
We study deterministic conditional rewrite systems, i.e. conditional rewrite systemswhere the extra variables are not totally free but 'input bounded'. If such a systemR is quasi-reductive then !R is decidable and terminating. We develop a critical paircriterion to prove confluence if R is quasi-reductive and strongly deterministic. In thiscase we prove that R is logical, i.e./!R==R holds. We apply our results to proveHorn clause programs to be uniquely terminating.This research was supported by the Deutsche Forschungsgemeinschaft, SFB 314, Project D4Jürgen Avenhaus; Carlos Loría-Sáenzpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/344Mon, 03 Apr 2000 00:00:00 +0200Distributing equational theorem proving
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/346
In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected and the less important results are forgotten. We describe some useful experts and explain in detail how they work together. We establish fairness criteria and so prove the distributed system to be both, complete and correct. We have implementedour system and show by non-trivial examples that drastical time speed-ups are possible for a cooperating team of experts compared to the time needed by the best expert in the team.Jürgen Avenhaus; Jörg Denzingerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/346Mon, 03 Apr 2000 00:00:00 +0200A Reduction Ordering for Higher-Order Terms
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/372
We investigate one of the classical problems of the theory ofterm rewriting, namely termination. We present an ordering for compar-ing higher-order terms that can be utilized for testing termination anddecreasingness of higher-order conditional term rewriting systems. Theordering relies on a first-order interpretation of higher-order terms anda suitable extension of the RPO.Jürgen Avenhaus; Carlos Loría-Sáenz; Joachim Steinbachpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/372Mon, 03 Apr 2000 00:00:00 +0200General Algorithms for Permutations in Equational Inference
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/377
We study some general algorithms for processing permutations and permu-tation groups and consider their application to equational reasoning and term-rewriting systems. We also present some complexity results for particular equa-tional consequence problems related to permutations.Jürgen Avenhaus; David A. Plaistedpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/377Mon, 03 Apr 2000 00:00:00 +0200Theorem Proving in Hierarchical Clausal Specifications
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/384
In this paper we are interested in an algebraic specification language that (1) allowsfor sufficient expessiveness, (2) admits a well-defined semantics, and (3) allows for formalproofs. To that end we study clausal specifications over built-in algebras. To keep thingssimple, we consider built-in algebras only that are given as the initial model of a Hornclause specification. On top of this Horn clause specification new operators are (partially)defined by positive/negative conditional equations. In the first part of the paper wedefine three types of semantics for such a hierarchical specification: model-theoretic,operational, and rewrite-based semantics. We show that all these semantics coincide,provided some restrictions are met. We associate a distinguished algebra A spec to ahierachical specification spec. This algebra is initial in the class of all models of spec.In the second part of the paper we study how to prove a theorem (a clause) valid in thedistinguished algebra A spec . We first present an abstract framework for inductive theoremprovers. Then we instantiate this framework for proving inductive validity. Finally wegive some examples to show how concrete proofs are carried out.This report was supported by the Deutsche Forschungsgemeinschaft, SFB 314 (D4-Projekt)Jürgen Avenhaus; Klaus Madlenerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/384Mon, 03 Apr 2000 00:00:00 +0200Informal Proceedings of the Annual Meeting of "GI-Fachgruppe Deduktionssysteme"
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/415
This report contains a collection of abstracts for talks given at the "Deduktionstreffen" held at Kaiserslautern, October 6 to 8, 1993. The topics of the talks range from theoretical aspects of term rewriting systems and higher order resolution to descriptions of practical proof systems in various applications. They are grouped together according the following classification: Distribution and Combination of Theorem Provers, Termination, Completion, Functional Programs, Inductive Theorem Proving, Automatic Theorem Proving, Proof Presentation. The Deduktionstreffen is the annual meeting of the Fachgruppe Deduktionssysteme in the Gesellschaft für Informatik (GI), the German association for computer science.Jürgen Avenhaus; Jörg Denzingerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/415Mon, 03 Apr 2000 00:00:00 +0200