A key ingredient of computational argumentation in AI is the generation of arguments in favor of or against claims under scrutiny. In this paper we look at the complexity of argument construction and reasoning in the prominent structured formalism of assumption-based argumentation (ABA). We point out that reasoning in ABA by means of constructing an abstract argumentation framework (AF) gives rise to two main sources of complexity: (i) constructing the AF and (ii) reasoning within the constructed graph. Since both steps are intractable in general, it is no surprise that the best performing state-of-the-art ABA reasoners skip the instantiation procedure entirely and perform tasks directly on the input knowledge base. Driven by this observation, we identify and study atomic and symmetric ABA, two ABA fragments that preserve the expressive power of general ABA, and that can be utilized to have milder complexity in the first or second step. We show that using atomic ABA allows for an instantiation procedure for general ABA leading to polynomially-bounded AFs and that symmetric ABA can be used to create AFs that have mild complexity to reason on. By an experimental evaluation, we show that using the former approach with modern AF solvers can be competitive with state-of-the-art ABA solvers, improving on previous AF instantiation approaches that are hindered by intractable argument construction.
{"title":"Argumentation Frameworks Induced by Assumption-Based Argumentation: Relating Size and Complexity","authors":"Anna Rapberger, Markus Ulbricht, J. Wallner","doi":"10.24963/kr.2023/43","DOIUrl":"https://doi.org/10.24963/kr.2023/43","url":null,"abstract":"A key ingredient of computational argumentation in AI is the generation of arguments in favor of or against claims under scrutiny. In this paper we look at the complexity of argument construction and reasoning in the prominent structured formalism of assumption-based argumentation (ABA). We point out that reasoning in ABA by means of constructing an abstract argumentation framework (AF) gives rise to two main sources of complexity: (i) constructing the AF and (ii) reasoning within the constructed graph. Since both steps are intractable in general, it is no surprise that the best performing state-of-the-art ABA reasoners skip the instantiation procedure entirely and perform tasks directly on the input knowledge base. Driven by this observation, we identify and study atomic and symmetric ABA, two ABA fragments that preserve the expressive power of general ABA, and that can be utilized to have milder complexity in the first or second step. We show that using atomic ABA allows for an instantiation procedure for general ABA leading to polynomially-bounded AFs and that symmetric ABA can be used to create AFs that have mild complexity to reason on. By an experimental evaluation, we show that using the former approach with modern AF solvers can be competitive with state-of-the-art ABA solvers, improving on previous AF instantiation approaches that are hindered by intractable argument construction.","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125923312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-28DOI: 10.48550/arXiv.2204.13305
M. Bernreiter, W. Dvořák, Anna Rapberger, S. Woltran
In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level rather than on the argument-level, while under certain natural restrictions (arguments with the same claims have the same outgoing attacks) these properties are conserved. We now investigate these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments. As we shall see, these reductions give rise to different classes of claim-augmented argumentation frameworks, and behave differently in terms of semantic properties and computational complexity. This strengthens the view that the actual choice for handling preferences has to be taken with care.
{"title":"The Effect of Preferences in Abstract Argumentation Under a Claim-Centric View","authors":"M. Bernreiter, W. Dvořák, Anna Rapberger, S. Woltran","doi":"10.48550/arXiv.2204.13305","DOIUrl":"https://doi.org/10.48550/arXiv.2204.13305","url":null,"abstract":"In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on \u0000 claim-level rather than on the argument-level, while under certain \u0000 natural restrictions (arguments with the same claims have the \u0000 same outgoing attacks) these properties are conserved. We now investigate\u0000 these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments.\u0000 As we shall see, these reductions give rise to \u0000 different classes of claim-augmented argumentation frameworks, and behave \u0000 differently in terms of semantic properties and computational complexity.\u0000 This strengthens the view that the actual choice for handling preferences \u0000 has to be taken with care.","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128881268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-09-27DOI: 10.1007/978-3-540-30227-8_39
S. Doutre, J. Mengin
{"title":"On sceptical vs credulous acceptance for abstract argument systems","authors":"S. Doutre, J. Mengin","doi":"10.1007/978-3-540-30227-8_39","DOIUrl":"https://doi.org/10.1007/978-3-540-30227-8_39","url":null,"abstract":"","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126497076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-06-18DOI: 10.1007/978-3-540-24836-1_11
Omar El-Khatib, Enrico Pontelli, Tran Cao Son
{"title":"ASP-PROLOG: a system for reasoning about answer set programs in prolog","authors":"Omar El-Khatib, Enrico Pontelli, Tran Cao Son","doi":"10.1007/978-3-540-24836-1_11","DOIUrl":"https://doi.org/10.1007/978-3-540-24836-1_11","url":null,"abstract":"","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125055837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-05-17DOI: 10.1007/978-3-540-24840-8_21
Richard A. Baldwin, E. Neufeld
{"title":"The structural model interpretation of the NESS test","authors":"Richard A. Baldwin, E. Neufeld","doi":"10.1007/978-3-540-24840-8_21","DOIUrl":"https://doi.org/10.1007/978-3-540-24840-8_21","url":null,"abstract":"","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114898125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-09-15DOI: 10.1007/978-3-540-39451-8_8
P. Besnard, Robert E. Mercer, Torsten Schaub
{"title":"Optimality theory through default logic","authors":"P. Besnard, Robert E. Mercer, Torsten Schaub","doi":"10.1007/978-3-540-39451-8_8","DOIUrl":"https://doi.org/10.1007/978-3-540-39451-8_8","url":null,"abstract":"","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130177564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-07-19DOI: 10.1007/3-540-45619-8_28
D. Pearce, Vladimir Sarsakov, Torsten Schaub, H. Tompits, S. Woltran
{"title":"A polynomial translation of logic programs with nested expressions into disjunctive logic programs: preliminary report","authors":"D. Pearce, Vladimir Sarsakov, Torsten Schaub, H. Tompits, S. Woltran","doi":"10.1007/3-540-45619-8_28","DOIUrl":"https://doi.org/10.1007/3-540-45619-8_28","url":null,"abstract":"","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134427640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-07-09DOI: 10.1007/978-3-540-24581-0_31
S. Chopra, J. Heidema, T. Meyer
{"title":"Some logics of belief and disbelief","authors":"S. Chopra, J. Heidema, T. Meyer","doi":"10.1007/978-3-540-24581-0_31","DOIUrl":"https://doi.org/10.1007/978-3-540-24581-0_31","url":null,"abstract":"","PeriodicalId":274824,"journal":{"name":"Non-Monotonic Reasoning","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125932615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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