ABA+: Assumption-Based Argumentation with Preferences

My work focuses on using argumentation theory to model common-sense reasoning with preferences. To this end, I have equipped a well-established structured argumentation formalism, Assumption-Based Argumentation, with a preference handling mechanism. I aim to advance the newly proposed formalism, called ABA, present its motivations and place among other argumentation formalisms, and discuss various properties of ABA. 1 Argumentation and Preferences Dealing with preferences is an important topic in AI at large, and argumentation in particular (Kaci 2011). A principal issue regarding argumentation and preferences is the lack of consensus on how preferences should be accounted for. This is witnessed by a large number of argumentation formalisms handling preferences in different ways. Most of these can be broadly classified with respect to several main methods. One method is to compile preferences into the object level, by encoding them within the existing components of a formalism: e.g. (Kowalski and Toni 1996; Thang and Luong 2014). Such an approach may, however, produce numerous additional objects from a compact preference relation (Wakaki 2014), and could be hard to generalize. Another method, utilized by a majority of argumentation formalisms dealing with preferences, e.g. (Prakken and Sartor 1999; Amgoud and Cayrol 2002; Bench-Capon 2003; Kaci and van der Torre 2008; Brewka and Woltran 2010; Besnard and Hunter 2014; Modgil and Prakken 2014; Garcı́a and Simari 2014), is to use preferences on the argument level to discard attacks from less preferred arguments: if an argument A attacks an argument B (written A B) but B is preferred over A (written A < B), then A B fails. This may be problematic, as, for instance, {A,B} can then be a subset of an acceptable extension, which would then not be conflict-free with respect to the original attack relation (see e.g. (Kaci 2010; Amgoud and Vesic 2014) for discussions). To avoid this issue, certain conditions can be imposed on argument frameworks: e.g. considering only symmetric attacks (Kaci 2010), contraposition on rules (Modgil and Prakken 2014). Such restrictions may, however, lead to other problems: e.g. rationality postulates unsatisfied, counterintuitive limitations on expressiveness (see e.g. (Amgoud and Vesic 2014; Baroni, Giacomin, and Liao 2015)). Yet another approach is to employ preferences on the extension level to select the most ‘preferable’ extensions, e.g. (Amgoud and Vesic 2011; Wakaki 2014). However, this may not always be adequate either. For example, if A,B are the only arguments and A B is the only attack, then {A} is the only (say, stable) extension to begin with, whence whatever the preferences over arguments, there is no choice to be made: even if A < B, {B} cannot be selected as the ‘preferable’ extension. Likewise, in the absence of extensions due to, for instance, odd cycles, preferences do not play a role. Both methods of discarding attacks and selecting among extensions due to preference information, often involve preference aggregation mechanisms: object-level (or argumentlevel) preferences are lifted to argumentor extension-levels by means of element set-wise comparison, e.g. (Kaci and van der Torre 2008; Modgil and Prakken 2014; Amgoud and Vesic 2011; 2014; Wakaki 2014). This entails outcome dependency on the choice of comparison principle. Finally, a couple of very recently proposed formalisms, namely (Rich) Preference-based Argumentation Frameworks (PAFs) (Amgoud and Vesic 2014) and AssumptionBased Argumentation with Preferences (ABA) (Čyras and Toni 2016a), represent the method of attack reversal. In PAFs, attacks are reversed in Abstract Argumentation (AA) (Dung 1995) setting: if A B and A < B, then A B fails and instead one obtains B A. ABA takes this idea further, to the realm of structured argumentation, by equipping Assumption-Based Argumentation (ABA) (Bondarenko et al. 1997; Toni 2014) with (object-level) preferences over assumptions and incorporating them directly into the attack relation so as to reverse attacks.