{"title":"基于假设的扩展断据逻辑编程论证及其与非单调推理的关系","authors":"T. Wakaki","doi":"10.3233/aac-220019","DOIUrl":null,"url":null,"abstract":"The motivation of this study is that Reiter’s default theory as well as assumption-based argumentation frameworks corresponding to default theories have difficulties in handling disjunctive information, while a disjunctive default theory (ddt) avoids them. This paper presents the semantic correspondence between generalized assumption-based argumentation (ABA) and extended disjunctive logic programming as well as the correspondence between ABA and nonmonotonic reasoning approaches such as disjunctive default logic and prioritized circumscription. To overcome the above-mentioned difficulties of ABA frameworks corresponding to default theories, we propose an assumption-based framework (ABF) translated from an extended disjunctive logic program (EDLP) since an EDLP can be translated into a ddt. Our ABF incorporates explicit negation and the connective of disjunction “|” to Heyninck and Arieli’s ABF induced by a disjunctive logic program. In this paper, first, we show how arguments are constructed from disjunctive rules in our proposed ABF. Then, we show the correspondence between answer sets of an EDLP P and stable extensions of the ABF translated from P with trivialization rules. After defining rationality postulates, we show answer sets of a consistent EDLP are captured by consistent stable extensions of the translated ABF with no trivialization rules. Finally, we show the correspondence between ABA and disjunctive default logic (resp. prioritized circumscription). The relation between ABA and possible model semantics of EDLPs is also discussed.","PeriodicalId":299930,"journal":{"name":"Argument & Computation","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Assumption-based argumentation for extended disjunctive logic programming and its relation to nonmonotonic reasoning\",\"authors\":\"T. Wakaki\",\"doi\":\"10.3233/aac-220019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The motivation of this study is that Reiter’s default theory as well as assumption-based argumentation frameworks corresponding to default theories have difficulties in handling disjunctive information, while a disjunctive default theory (ddt) avoids them. This paper presents the semantic correspondence between generalized assumption-based argumentation (ABA) and extended disjunctive logic programming as well as the correspondence between ABA and nonmonotonic reasoning approaches such as disjunctive default logic and prioritized circumscription. To overcome the above-mentioned difficulties of ABA frameworks corresponding to default theories, we propose an assumption-based framework (ABF) translated from an extended disjunctive logic program (EDLP) since an EDLP can be translated into a ddt. Our ABF incorporates explicit negation and the connective of disjunction “|” to Heyninck and Arieli’s ABF induced by a disjunctive logic program. In this paper, first, we show how arguments are constructed from disjunctive rules in our proposed ABF. Then, we show the correspondence between answer sets of an EDLP P and stable extensions of the ABF translated from P with trivialization rules. After defining rationality postulates, we show answer sets of a consistent EDLP are captured by consistent stable extensions of the translated ABF with no trivialization rules. Finally, we show the correspondence between ABA and disjunctive default logic (resp. prioritized circumscription). The relation between ABA and possible model semantics of EDLPs is also discussed.\",\"PeriodicalId\":299930,\"journal\":{\"name\":\"Argument & Computation\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Argument & Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3233/aac-220019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Argument & Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/aac-220019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本研究的动机在于,Reiter 的缺省理论以及与缺省理论相对应的基于假设的论证框架在处理断点信息时存在困难,而断点缺省理论(ddt)则可以避免这些困难。本文介绍了广义的基于假设的论证(ABA)与扩展的缺省逻辑编程之间的语义对应关系,以及 ABA 与非单调推理方法(如缺省逻辑和优先化周延)之间的对应关系。为了克服与缺省理论相对应的 ABA 框架的上述困难,我们提出了一种基于假设的框架(ABF),该框架由扩展断言逻辑程序(EDLP)转化而来,因为 EDLP 可以转化为 ddt。我们的 ABF 将显式否定和析取连接词"|"纳入了海宁克(Heyninck)和阿里里(Arieli)的 ABF,该 ABF 由析取逻辑程序诱导而成。在本文中,我们首先展示了在我们提出的 ABF 中,参数是如何从非谓词规则中构造出来的。然后,我们展示了 EDLP P 的答案集与用三段论规则从 P 翻译而来的 ABF 的稳定扩展之间的对应关系。在定义了合理性假设之后,我们证明了一致的 EDLP 答案集可以通过无琐碎化规则的 ABF 译文的一致稳定扩展来捕捉。最后,我们展示了 ABA 与分条件缺省逻辑(即优先周延)之间的对应关系。我们还讨论了 ABA 与 EDLP 可能的模型语义之间的关系。
Assumption-based argumentation for extended disjunctive logic programming and its relation to nonmonotonic reasoning
The motivation of this study is that Reiter’s default theory as well as assumption-based argumentation frameworks corresponding to default theories have difficulties in handling disjunctive information, while a disjunctive default theory (ddt) avoids them. This paper presents the semantic correspondence between generalized assumption-based argumentation (ABA) and extended disjunctive logic programming as well as the correspondence between ABA and nonmonotonic reasoning approaches such as disjunctive default logic and prioritized circumscription. To overcome the above-mentioned difficulties of ABA frameworks corresponding to default theories, we propose an assumption-based framework (ABF) translated from an extended disjunctive logic program (EDLP) since an EDLP can be translated into a ddt. Our ABF incorporates explicit negation and the connective of disjunction “|” to Heyninck and Arieli’s ABF induced by a disjunctive logic program. In this paper, first, we show how arguments are constructed from disjunctive rules in our proposed ABF. Then, we show the correspondence between answer sets of an EDLP P and stable extensions of the ABF translated from P with trivialization rules. After defining rationality postulates, we show answer sets of a consistent EDLP are captured by consistent stable extensions of the translated ABF with no trivialization rules. Finally, we show the correspondence between ABA and disjunctive default logic (resp. prioritized circumscription). The relation between ABA and possible model semantics of EDLPs is also discussed.