{"title":"Non-termination in Term Rewriting and Logic Programming","authors":"Étienne Payet","doi":"10.1007/s10817-023-09693-z","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we define two particular forms of non-termination, namely <i>loops</i> and <i>binary chains</i>, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of <i>compatibility</i> of binary relations. We also present a syntactic criterion for the detection of a special case of binary chains. Moreover, we describe our implementation <span>NTI</span> and compare its results at the Termination Competition 2023 with those of leading analyzers.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"13 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Automated Reasoning","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10817-023-09693-z","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility of binary relations. We also present a syntactic criterion for the detection of a special case of binary chains. Moreover, we describe our implementation NTI and compare its results at the Termination Competition 2023 with those of leading analyzers.
期刊介绍：
The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning.
The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.
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