Beierle, Christoph (Fern Universität) | Kutsch, Steven (Fern Universität) | Breuers, Henning (Fern Universität)

Reasoning in the context of a conditional knowledge base containing rules of the form'If A then usually B' can be defined in terms of preference relations on possible worlds. These preference relations can be modeled by ranking functions that assign a degree of disbelief to each possible world. In general, there are multiple ranking functions that accept a given knowledge base. Several nonmonotonic inference relations have been proposed using c-representations, a subset of all ranking functions. These inference relations take subsets of all c-representations based on various notions of minimality into account, and they operate in different inference modes, i.e., skeptical, weakly skeptical, or credulous. For nonmonotonic inference relations, weaker versions of monotonicity like rational monotony (RM) and weak rational monotony (WRM) have been developed. In this paper, we investigate which of the inference relations induced by sets of minimal c-representations satisfy rational monotony or weak rational monotony.

Beierle, Christoph (University of Hagen) | Kutsch, Steven (University of Hagen) | Obergrusberger, Andreas (University of Hagen)

Various semantics have been developed for knowledge bases consisting of qualitative conditionals representing default rules. Recently, skeptical, weakly skeptical, and credulous inference relations based on c-representations and taking classes of preferred models into account have been proposed. In this paper, we investigate their interrelationships and solve several open problems regarding these interrelationships. In particular, we prove that the preferred models obtained from three different notions of minimality lead to pairwise distinct inference relations, and that none of them is able to exactly capture skeptical c-inference over all c-representations.

This article provides an experimental analysis of the possibilistic handling of default rules. Three different nonmonotonic consequence relations are considered: minimum specificity inference (MSP), lexicographical closure (LC), and epsilon-belief functions (LCD). The latter was initially proposed within the belief function framework; it is rephrased here within a possibility theory framework. These three consequence relations share some properties but differ on others, which allows for an experimental test of their psychological plausibility.

Clearly, the second approach is more cautious. Intuitively, it demands that there is a specific argument for τ that is contained in each rational stance a reasoner can take given Γ, DRules, and SRules. The first option doesn't bind the acceptability of τ to a specific argument: it is sufficient if according to each rational stance there is some argument for τ. In Default Logic, the main representational tool is that of a default rule, or simply a default.

Booth, Richard (University of Luxembourg) | Kaci, Souhila (University of Montpellier 2) | Rienstra, Tjitze (University of Luxembourg) | Torre, Leendert van der (University of Luxembourg)

We present 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 study 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 study a non-monotonic type of inference which allows counterfactual inferences. We precisely characterize the classes of frameworks distinguishable by the non-monotonic inference relation for the admissible semantics.