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Goal Oriented Equational Theorem Proving Using Team Work
 University of Kaiserslautern
, 1994
"... The team work method is a concept for distributing automated theorem provers and so to activate several experts to work on a given problem. We have implemented this for pure equational logic using the unfailing KnuthBendix completion procedure as basic prover. In this paper we present three classes ..."
Abstract

Cited by 25 (12 self)
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The team work method is a concept for distributing automated theorem provers and so to activate several experts to work on a given problem. We have implemented this for pure equational logic using the unfailing KnuthBendix completion procedure as basic prover. In this paper we present three classes of experts working in a goal oriented fashion. In general, goal oriented experts perform their job "unfair" and so are often unable to solve a given problem alone. However, as a team member in the team work method they perform highly efficient, even in comparison with such respected provers as Otter 3.0 or REVEAL, as we demonstrate by examples, some of which can only be proved using team work. The reason for these achievements results from the fact that the team work method forces the experts to compete for a while and then to cooperate by exchanging their best results. This allows one to collect "good" intermediate results and to forget "useless" ones. Completion based proof methods are fr...
A Methodology for Equational Reasoning
 In: Hawaii International Conference on System Sciences 27, Eds
, 1994
"... 1 This paper presents a methodology to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use attributes of terms and heuristics to determine bridge lemmas, i.e. lemmas which have to be used during the proof of the ..."
Abstract

Cited by 14 (7 self)
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1 This paper presents a methodology to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use attributes of terms and heuristics to determine bridge lemmas, i.e. lemmas which have to be used during the proof of the theorem. Once we have found such a bridge lemma we use the techniques of difference unification and rippling to enable its use. 1 Introduction Automated theorem provers suffer from their inability or inefficiency in solving problems. This effect is especially the case if equality is included. The most promising approach to mechanize equality reasoning stems from Knuth and Bendix [13] who restricted the application of equations (by using them as rewrite rules) and formulated their completion calculus which led to an considerable decrease of the search space. The original completion procedure of Knuth and Bendix is restricted to directable unit equations. This strong restriction was weakene...