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Combining Extension-Based Semantics and Ranking-Based Semantics for Abstract Argumentation Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, Nicolas Maudet

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Combining Extension-Based Semantics and Ranking-Based Semantics for Abstract Argumentation Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, Nicolas Maudet Combining Extension-based Semantics and Ranking-based Semantics for Abstract Argumentation Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, Nicolas Maudet To cite this version: Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, Nicolas Maudet. Combining Extension-based Semantics and Ranking-based Semantics for Abstract Argumentation. 16th International Conference on Principles of Knowledge Representation and Reasoning, Oct 2018, Tempe, United States. hal- 01900735 HAL Id: hal-01900735 https://hal.archives-ouvertes.fr/hal-01900735 Submitted on 22 Oct 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Combining Extension-based Semantics and Ranking-based Semantics for Abstract Argumentation Elise Bonzon Jer´ omeˆ Delobelle Sebastien´ Konieczny Nicolas Maudet LIPADE CRIL, CNRS LIP6, CNRS Universite´ Paris Descartes, France Universite´ d’Artois, France Sorbonne Universite,´ 75005 Paris, France [email protected] fdelobelle,[email protected] [email protected] Abstract and Lagasquie-Schiex 2005; Amgoud and Ben-Naim 2013; Grossi and Modgil 2015; Pu et al. 2015; Amgoud et al. 2016; Two kinds of semantics exist for abstract argumentation. Patkos, Bikakis, and Flouris 2016; Bonzon et al. 2016b)), Extension-based semantics evaluate the acceptability of sets where the aim is to (comparatively) evaluate each argu- of arguments, while ranking-based semantics evaluate the strength of each argument. They focus on different aspects ment in an argumentation system. Ranking-based semantics of the information conveyed by argumentation systems. Af- are functions that map each argumentation framework to a ter discussing pros and cons of both approaches, we study ranking (usually a total pre-order) on its arguments. This how to combine them, in order to take benefits from both. We ranking represents the comparative strength of each argu- propose six new families of semantics for abstract argumen- ment. Thus, conversely to extension-based (and labelling- tation combining extension-based and ranking-based seman- based) semantics, this approach does not evaluate sets of tics. More precisely we propose to refine the ranking-based arguments but each argument individually, based on its sit- semantics using information coming from extension-based uation in the argumentation graph. A related kind of se- semantics acceptability of arguments, and to modify the ex- mantics are grading-based semantics (see e.g. (Besnard and tensions chosen by extension-based semantics using prefer- Hunter 2001; Matt and Toni 2008; Leite and Martins 2011; ential information coming from ranking-based semantics. da Costa Pereira, Tettamanzi, and Villata 2011)), where a numerical value is assigned to each argument. The evalua- Introduction tion is numerical instead of ordinal, but the aim is still to evaluate each argument individually. Clearly, if one defines Argumentation is the process of confronting conflicting ar- a grading-based semantics, then this straightforwardly in- guments. In the abstract argumentation framework (Dung duces a corresponding ranking-based semantics. 1995), the classical semantics are extension-based seman- tics. These semantics aim at evaluating which sets of argu- Thus we may opt for two kinds of evaluations of argu- ments can be accepted together. These extensions are usually ments: at the level of set of arguments (with extension-based based on the conflict-freeness principle (two arguments in an or labelling-based semantics) or at the level of single ar- extension can not attack each other) and on the self-defense guments (with ranking-based or grading-based semantics). principle (an extension has to defend each of its attacked ar- These two ways to evaluate the information encoded in an gument). Thus, these semantics evaluate sets of arguments argumentation framework are interesting, and are useful for in a binary way (sets of arguments are or are not extensions different applications. The second approach is much more for a given semantics). recent and more work is needed to better understand the no- In (Caminada 2006), labelling-based semantics have been tions and look for meaningful new semantics. But even the introduced to associate different labellings to the arguments first kind of evaluation, although studied for a long time, still of any argumentation framework. A labelling is a function need some work for understanding their underlying princi- that maps each argument to the set fin; out; undecg, where ples (it worths mentioning that conversely to other reasoning in means that the argument is accepted for the labelling, out tasks like inference (Kraus, Lehmann, and Magidor 1990; means that the argument is rejected, and undec means that Makinson 1994) or revision (Alchourron,´ Gardenfors,¨ and the argument is undecided. So these semantics still perform Makinson 1985; Gardenfors¨ 1988; Katsuno and Mendelzon an evaluation of sets of arguments, just like extension-based 1991), there are no postulates for characterizing rational ar- semantics. And it has been shown that all extension-based gumentation semantics and no representation theorem). semantics correspond to some labelling-based semantics. The starting point of this work is the observation that More recently, it has been argued that this binary or these two kinds of evaluation are in a sense orthogonal. They ternary evaluation can be too rough for some applica- both can be used to extract some information about the sta- tions, for example for online debate platforms (Leite and tus/strength/situation of (sets of) arguments. Instead of see- Martins 2011), and the need of a more focused evalu- ing these approaches as mutually exclusive, one natural idea ation of each argument has been put forward. This led is to try to take the best of both worlds and combine them. to the idea of ranking-based semantics (see e.g. (Cayrol We believe that studying the potential of such a combination, as we initiate in this work, can be very fruitful for developing between arguments and thus obtain a consistent set of for- argumentation semantics. mulas. In this work we propose six new families of semantics However, in other applications, some of these proper- for abstract argumentation combining extension-based se- ties can be discussed. Recently, online debate platforms are mantics and ranking-based semantics. More precisely, we emerging on the internet. On these debate platforms, agents propose to refine ranking-based semantics using information argue for or against a particular topic (in the form of a coming from extension-based semantics acceptability of ar- question or an affirmation) or other existing arguments. Of- guments, and to modify the extensions chosen by extension- ten, the goal is not to find the arguments which can be ac- based semantics using preferential information coming from cepted together but to evaluate how accepted is the ques- ranking-based semantics. tion/affirmation. But more generally, when one faces many More precisely in the next section we will discuss the arguments, having a more detailed evaluation of arguments differences between the evaluation of arguments obtained than the binary accepted/rejected obtained with extension- by extension-based semantics and ranking-based semantics. based semantics may be useful. Leite and Martins (2011) We will then recall the necessary background on abstract emphasize the limitations of classical acceptability seman- argumentation. We will next show how to modify ranking- tics for this kind of applications. In addition, to accurately based semantics by taking into account information coming represent the opinions of thousands of users, it could be from extension-based semantics. We propose four ways to more appropriate to evaluate arguments using degrees of do that. The first one is by focusing only on the acceptabil- acceptability or gradual acceptability. With ranking-based ity status of each argument (given by the extension-based semantics, we can precisely obtain a very detailed evalua- semantics). The second one is based on a more precise eval- tion of the strength of each argument. This can be useful for uation of the acceptability status of each argument from (Wu these debate platforms, but also to select best arguments in and Caminada 2010). The third and fourth ones are modifi- all kinds of debates (persuasion, deliberation, etc.). cations of a particular ranking-based method, the Propaga- However we can see as a drawback the fact that the eval- tion method (Bonzon et al. 2016b), where we allow a more uation of each argument is not linked at all with its ac- fined-gained distinction of arguments using these accept- ceptance status: being an argument with a good evaluation ability status. Concerning the other way, i.e. how to modify does not mean that this argument should be accepted (un- extension-based semantics using ranking-based semantics, der extension-based semantics), and even if we define “ac- we show first that ranking-based semantics can be used to ceptance” with respect to the ranking, there are no natural evaluate
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