Mathematical Sciences: Toward a Theory of Well-Founded Orderings for Use in Automated Deduction

9510164约翰良好的排序在自动演绎中无处不在，这是开发基于重写的演绎系统中计算的终止证明以及旨在饱和过程中限制搜索空间的演绎策略的基础。然而，确定适用于特定目的的有理有据的排序通常需要大量的技术专门知识，而且由于重写的终止一般是不可决定的，所以最好的希望是对足够种类的排序有足够的了解，以便能够处理实践中出现的各种终止和效率问题。这项研究计划拨款致力于发展一种基于逻辑和数字不变量的有理有据的排序的全面理论。进一步研究的两个具体方向是将已知的结果扩展到更大的项类，以及对于更一般的有充分基础的排序，如指数排序，获得类似的结果。作为进一步的、相关的研究方向，我们将探索非完全良基排序的理论。由于顺序类型的概念对于非全排序没有意义，因此需要确定适当的逻辑不变量。***

9510164 Johann Well-founded orderings are ubiquitous in automated deduction, being fundamental to the development of termination proofs for computations in rewrite-based deduction systems, as well as of deduction strategies aiming to restrict search spaces in saturation processes. The determination of well-founded orderings suitable for a particular purpose, however, typically requires a good deal of technical expertise, and because termination of rewriting is undecidable in general the best that can be hoped for is to have a sufficient understanding of a sufficient variety of orderings to be able to cope with the many kinds of termination and efficiency problems which occur in practice. This research planning grant undertakes to develop a comprehensive theory of well-founded orderings based on their logical and numerical invariants. Two specific directions for further research are extending known results to larger classes of terms, and obtaining similar results for more general well- founded orderings, such as exponential orderings. As a further, related line of inquiry, a theory of nontotal well-founded orderings will be explored. Since the notion of order type makes no sense for nontotal orderings, appropriate logical invariants will need to be determined. ***