Section: New Results
Reasoning with Imperfect Information and Priorities
Participants : Madalina Croitoru, Jérôme Fortin, Souhila Kaci, Tjitze Rienstra, Rallou Thomopoulos.
Monotonic and Nonmonotonic Inference for Abstract Argumentation
An argumentation framework (or framework, for short) consists of a set of arguments, whose content may be left unspecified, together with an attack relation encoding conflict between arguments. Given a framework, a semantics specifies which sets of arguments (called extensions) are rationally acceptable. This formalism captures many different types of reasoning considered in the area of AI. In many applications, a framework somehow represents (part of) an agent's belief state. Beliefs are then formed on the basis of acceptable sets of arguments. For example, a `grounded reasoner' forms beliefs on the basis of the framework's grounded extension, a `preferred reasoner' on the basis of the preferred extensions, and so on. There is a problem with this account, however. Two different argumentation frameworks may be considered equivalent as soon as they lead to the same extensions. A more appropriate notion of equivalence is strong equivalence. Given a semantics, two frameworks are said to be strongly equivalent if their extensions are the same given every possible addition of new arguments and attacks. But still, it leaves open the question of how to form beliefs on the basis of a framework, so that different frameworks can be meaningfully distinguished, even if their extensions are the same. We addressed this problem and presented a new approach to reasoning about the outcome of an argumentation framework, where an agent's reasoning with a framework and semantics is represented by an inference relation defined over a logical labeling language. We first studied a monotonic type of inference which is, in a sense, more general than an acceptance function, but equally expressive. In order to overcome the limitations of this expressiveness, we studied a nonmonotonic type of inference which allows counterfactual inferences. We precisely characterized the classes of frameworks distinguishable by the nonmonotonic inference relation for the admissible semantics.

Joint work with R. Booth and L. van der Torre (Univ. of Luxembourg), published in FLAIRS 2013 [27]
Dynamics in Abstract Argumentation
Recent years have seen a considerable work on dynamics in argumentation framework (AF). We addressed dynamics in abstract argumentation using a logical theory where an agent's belief state consists of an argumentation framework and a constraint that encodes the outcome the agent believes the argumentation framework should have. Dynamics enters in two ways: (1) the constraint is strengthened upon learning that the AF should have a certain outcome and (2) the argumentation framework is expanded upon learning about new arguments/attacks. A problem faced in this setting is that a constraint may be inconsistent with the AF's outcome. We discussed two ways to address this problem: First, it is still possible to form consistent fallback beliefs, i.e., beliefs that are most plausible given the agent's argumentation framework and constraint. Second, we showed that it is always possible to find argumentation framework expansions to restore consistency. Our work combines various individual approaches in the literature on argumentation dynamics in a general setting.

Joint work with R. Booth and L. van der Torre (Univ. of Luxembourg), published in SUM 2013. [26]
Preferences have been intensively studied in argumentation framework. Preferencebased argumentation frameworks are instantiation of Dung's framework in which the defeat relation (in the sense of Dung) is computed from an attack relation and a preference relation over the set of arguments. We distinguish between different ways to derive preferences over arguments, e.g., from their relative specificity, relative strength or from values promoted by the arguments. However an underexposed aspect in these models is change of preferences. We proposed a dynamic model of preferences in argumentation, centering on what we call propertybased AFs. It is based on Dietrich and List's model of propertybased preference and it provides an account of how and why preferences in argumentation may change. The idea is that preferences over arguments are derived from preferences over properties of arguments, and change as the result of moving to different motivational states. We also provided a dialogical proof theory that establishes whether there exists some motivational state in which an argument is accepted.
Representing Synergy Among Arguments with Choquet Integral
Preferencebased argumentation frameworks are instantiation of Dung's framework in which the defeat relation (in the sense of Dung) is computed from an attack relation and a preference relation over the set of arguments. Valuebased argumentation framework is a preferencebased argumentation framework where the preference relation over arguments is derived from a preference relation over values they promote. We extended valuebased argumentation framework with collective defeats and arguments promoting values with various strengths. In the extended framework, we defined a function which computes the strength of a collective defeat. We also defined desired properties for the proposed function. Surprisingly, we showed that this function obeying the corresponding properties is Choquet integral, a wellknown aggregation function at work in multiple criteria decision.

Joint work with C. Labreuche (Thales), published in ECSQARU 2013 [35]
Compiling Preference Queries in Qualitative Constraint Problems
Comparative preference statements are the basic ingredients of conditional logics for representing users' preferences in a compact way. These statements may be strict or not and obey different semantics. Algorithms have been developed in the literature to compute a preference relation over outcomes given a set of comparative preference statements and one or several semantics. These algorithms are based on insights from nonmonotonic reasoning (more specifically, minimal and maximal specificity principles) enforcing the preference relations to be a complete preorder. The main limitation of these logics however relies in preference queries when comparing two outcomes. Indeed given two outcomes having the same preference w.r.t. the preference relation, there is no indication whether this equality results from an equality between two preference statements or the outcomes are in fact incomparable and equality has been enforced by specificity principles. On the other hand, comparative preference statements and their associated semantics can be translated into qualitative constraint satisfaction problems in which one can have a precise ordering over two outcomes. We investigated this bridge and provided a compilation of conditional logicsbased preference queries in qualitative constraint problems.

Joint work with J.F. Condotta (CRIL), published in FLAIRS 2013 [31]
Argumentation for Reasoning with Inconsistencies
We investigate the use of argumentation when reasoning over an inconsistent knowledge base. We use argumentation in this context given the explanation power that it may bring (and that is currently under investigation).
We have investigated logical based argumentation following two methods. First, we have defined our own argument and attack notion (given the logical language at hand) and showed that such instantiation respects desirable properties of consistency and maximality (called rationality postulates in the field). This work has showed that the ICR, AR, IAR semantics investigated by inconsistent query answering (see Pagoda, Section 8.1 ) are the same as skeptically preferred or stable semantics, grounded and universally stable or preferred. Such result is encouraging as it bridges the two communities (argumentation and inconsistent query answering) allowing to use results from one field in order to enrich the other. We have also investigated the practical applicability of such argument definition and approach in the selection of flour for bread.
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On the other hand we have also looked at using a generic logical argumentation framework (ASPIC) in order to instantiate it with a simple logic in the EcoBioCap project (see Section 8.2 ). We have extended previous results to enrich bipolar queries. A software tool is under construction.

Work published in RIA 2013 [21]