Argumentation theory and its application to reasoning under inconsistency – keynote at GKR 2017– Srdjan Vesic CRIL, CNRS - Univ. Artois, Lens, France [email protected] 1 Argumentation theory Argumentation is a reasoning model based on construction and evaluation of arguments and attacks between them. Arguments are present, for example, in debates, essays or negotiations. An enormous amount of arguments is created every day as a part of customer feed-back on online selling platforms, where users comment on positive and negative features of products. More structured arguments are produced as a part of platforms like debategraph1 and arguman2. Most of the computational models of arguments in computer science and artificial intelligence are influenced by the model of Dung (1995), which sees an argumentation framework as a directed graph whose nodes are arguments and edges attacks between them. This model can be enriched by adding supports between arguments (Amgoud et al., 2008; Nouioua and Risch, 2011; Brewka et al., 2013), intrinsic strengths of ar- guments (Amgoud and Cayrol, 2002; Bench-Capon, 2003; Amgoud and Vesic, 2011) or strengths of attacks (Dunne et al., 2011). In order to know which arguments to accept, different semantics were introduced. Extension-based semantics (e.g. stable, preferred) return sets of sets of arguments. More than 20 semantics were introduced in the literature. In order to choose and eval- uate semantics, different principles were introduced (Baroni and Giacomin, 2007). Under extension-based semantics, one attack has the same effect as several attacks. This makes perfect sense in some applications. However, it is often the case that an at- tack does not completely destroy its target, but only weakens it. This kind of situation is modelled by ranking-based semantics (Besnard and Hunter, 2001; da Costa Pereira et al., 2011; Pu et al., 2014; Amgoud et al., 2016). Principles for ranking-based seman- tics were also introduced (Amgoud and Ben-Naim, 2013). 1http://debategraph.org/ 2http://en.arguman.org 0 2 Using argumentation for reasoning under inconsis- tency Given an inconsistent knowledge base, argumentation can be used to obtain non-trivial conclusions. Cayrol (1995) shows that there is a correspondence between the maximal consistent subsets of a knowledge base and the conclusions of stable extensions of the argumentation graph generated from that knowledge base. Of course, the choice of at- tack relation influences the result. Some attack relations are shown to yield inconsistent results that violate the principles for instantiated argumentation systems (Caminada and Amgoud, 2007). The question is: can the use of argumentation yield another (“more interesting”) re- sult? Recent work by Amgoud and Ben-Naim (2015) shows that using ranking-based semantics can be a useful tool for inferring under inconsistency. Their framework re- turns conclusions in the form of a stratified knowledge base. Roughly speaking, the idea is that the formulas that appear in some conflicts are preferred to formulas that appear in many conflicts. Their framework satisfies several desirable principles. Con- sistency says that if the knowledge base is consistent, the conclusions of the corre- sponding argumentation system are equal to the closure of the knowledge base. Flat- ness says that if the knowledge base is consistent, the conclusions of the corresponding argumentation system are all equally preferred. Non-trivialization says that the set of conclusions of the argumentation system is never trivial (i.e. it is never equal to the set of all formulas of the given logic). Free precedence says that the free formulas (i.e. the formulas that do not appear in any minimal unsatisfiable subset of the knowledge base) are the most preferred conclusions of the corresponding argumentation system. Dominance says that for two formulas ' and , if ' ` then is ranked better than ' in the corresponding argumentation system. The framework of Amgoud and Ben-Naim (2015) shows that argumentation and in particular ranking-based semantics offer an powerful tool for reasoning under incon- sistency. When using such an approach, in order to avoid generating infinitely many arguments, one has to define an equivalence relation between arguments and to gener- ate exactly one argument from each equivalence class. Yun et al. (2017) show that the choice of this equivalence relation has an impact on the final result. Thus, in addition to the choice of attack relation and semantics, one has to carefully choose this equivalence relation in order to obtain a meaningful result. 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