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

9510164 Johann良基排序在自动演绎中无处不在，对于基于重写的演绎系统中的计算的终止证明的开发以及旨在限制饱和过程中的搜索空间的演绎策略的开发是基础。 然而，确定适合于特定目的的有根据的排序通常需要大量的专业技术知识，并且由于重写的终止一般是不可判定的，因此可以希望的最好情况是对足够多的排序有足够的理解，以便能够处理实践中发生的多种终止和效率问题。 这项研究计划补助金承诺开发一个全面的理论，有理有据的排序的基础上，他们的逻辑和数值不变量。 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，并对更一般的良基序（如指数序）获得类似的结果。作为一个进一步的，相关的调查路线，非完全良基序的理论将进行探讨。 由于序类型的概念对非全序没有意义，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. ***