{"title":"Non-deterministic Approximation Operators: Ultimate Operators, Semi-equilibrium Semantics, and Aggregates","authors":"JESSE HEYNINCK, BART BOGAERTS","doi":"10.1017/s1471068423000236","DOIUrl":null,"url":null,"abstract":"Abstract Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, that is, operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola et al ., and (3) we generalize the characterizations of disjunctive logic programs to disjunctive logic programs with aggregates.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"42 1","pages":"0"},"PeriodicalIF":1.4000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory and Practice of Logic Programming","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s1471068423000236","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, that is, operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola et al ., and (3) we generalize the characterizations of disjunctive logic programs to disjunctive logic programs with aggregates.
期刊介绍：
Theory and Practice of Logic Programming emphasises both the theory and practice of logic programming. Logic programming applies to all areas of artificial intelligence and computer science and is fundamental to them. Among the topics covered are AI applications that use logic programming, logic programming methodologies, specification, analysis and verification of systems, inductive logic programming, multi-relational data mining, natural language processing, knowledge representation, non-monotonic reasoning, semantic web reasoning, databases, implementations and architectures and constraint logic programming.
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