In this paper, we place ourselves in the Ontology Based Data Access (OBDA) setting and investigate reasoning with inconsistent existential rules knowledge bases. We use the notion of inconsistency measures on sets of facts to rank and filter repairs. We propose a generic framework to answer queries by using the best repairs and study productivity and properties of such a framework.

Bruno Yun), pierre.bisquert@inra.fr (Pierre Bisquert), patrice.buche@inra.fr (Patrice Buche), croitoru@lirmm.fr (Madalina Croitoru), guillard@univ-montp2.fr (Valérie Guillard), rallou.thomopoulos@inra.fr (Rallou Thomopoulos) Abstract 13 Food packaging plays a crucial part in the post-harvest environmental im-14 pact of fresh foods. Packaging is usually wrongly considered as additional 15 economical and environmental costs. However, by minimizing food waste 16 and losses, it could significantly contribute to decrease the overall environ-17 mental impact of the food itself. A good balance between environmental 18 burden (resource consumption and additional waste management issues) and 19 real benefit in usage condition (reduction of food losses) should be thus de-20 fined when dimensioning a packaging for a given application. Beyond food 21 waste and environmental impact reduction, various kinds of considerations 22 about packaging, sometimes conflicting, are generally expressed by the stake-23 holders (food and packaging industries, health authorities, consumers, waste 24 management authority, etc.) related to safety, practicality, perceptions of 25 the packaging material, etc. Therefore, to help the parties deciphering all 26 these arguments, we designed an argumentation-based tool to take into ac-27 count the conflicting preferences expressed. The requirements concerning 28 Email addresses: yun@lirmm.fr (Bruno Yun), pierre.bisquert@inra.fr (Pierre Bisquert), patrice.buche@inra.fr (Patrice Buche), croitoru@lirmm.fr (Madalina Croitoru), guillard@univ-montp2.fr (Valérie Guillard), rallou.thomopoulos@inra.fr (Rallou Thomopoulos) packagings are modeled by several arguments provided by the stakeholders 29 expressing their viewpoints and expertise. Based on a new attack relation, 30 the argumentation tool computes sets of compatible arguments which are 31 used to rank alternative packagings under debate. In this paper, we present 32 a complete workflow implemented as a software prototype starting by defin-33 ing a structured representation of experts arguments and poll results, and 34 ending by a ranking of packaging solutions. We show and discuss the re-35 sults obtained by the software on a use case study (fresh strawberries) to 36 determine the justifiable choices between several packaging materials based 37 on stakeholders' arguments.38

Argumentation is a process of evaluating and comparing sets of arguments. Ranking-based semantics received a lot of attention recently. All of the semantics introduced so far are applicable to binary attack relations. In this paper, we study a more general case when sets of arguments can jointly attack an argument. We generalise existing postulates for ranking-based semantics to fit this framework, define a general variant of h-categoriser, prove that it converges for every argumentation framework and study the postulates it satisfies. We also study the link between binary and hypergraph version of h-categoriser.

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