Abstract Models of Transfinite Reductions

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We investigate transfinite reductions in abstract reduction systems. To this end, we study two abstract models for transfinite reductions: a metric model generalising the usual metric approach to infinitary term rewriting and a novel partial order model. For both models we distinguish between a weak and a strong variant of convergence as known from infinitary term rewriting. Furthermore, we introduce an axiomatic model of reductions that is general enough to cover all of these models of transfinite reductions as well as the ordinary model of finite reductions. It is shown that, in this unifying axiomatic model, many basic relations between termination and confluence properties known from finite reductions still hold. The introduced models are applied to term rewriting but also to term graph rewriting. We can show that for both term rewriting as well as for term graph rewriting the partial order model forms a conservative extension to the metric model.
Original languageUndefined/Unknown
Title of host publicationProceedings of the 21st International Conference on Rewriting Techniques and Applications
EditorsChristopher Lynch
Number of pages18
Place of PublicationDagstuhl, Germany
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH
Publication date2010
ISBN (Print)978-3-939897-18-7
Publication statusPublished - 2010


  • Transfinite reductions
  • Abstract reduction systems
  • Infinitary term rewriting
  • Metric model
  • Partial order model

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