自顶向下和自自底向上的定理证明器的协作
Cooperation between Top-Down and Bottom-Up Theorem Provers
摘要：
自顶向下和自自底向上的【形】的定理证明方法各有其优缺点。自底向上的【形】证明器得益于强冗余控制，但缺乏目标导向，而自顶向下的证明器是目标导向的，但往往有弱演算时，他们的证明长度被认为是。为了整合这两种方法，我们试图实现自上而下和自自底向上的【形】的证明器之间的合作，在两种不同的方式：第一种技术的目的是支持自自底向上的【形】的自上而下的证明器。自顶向下的证明器生成子目标子句，然后由自自底向上的【形】的证明器进行处理。第二种技术是在自顶向下的证明器中使用自自底向上的【形】生成的引理。我们将我们的概念应用于模型消除和叠加领域。我们讨论了我们的技术，以缩短证明，以及重新排序的搜索空间以适当的方式的能力。此外，为了确定子目标条款和引理，这实际上是相关的证明任务，我们开发了一个基于相关性的过滤方法。与证明SETHEO和SPASS在问题库TPTP中进行的实验揭示了我们的合作方法的高潜力。
英文摘要：
Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches.
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