Modgil, Sanjay, Prakken, Henry

This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC+'s modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung's framework and its extensions to accommodate preferences.

Prakken, Henry (Utrecht University and University of Groningen)

This paper investigates the relation between abstract and structured accounts of probabilistic argumentation. The ASPIC+ framework is applied to default reasoning with probabilistic generalisations, using the idea that the probability of an argument is the probability of the conjunction of all its premises and conclusions. Based on this idea, two notions of internal and dialectical argument strength are defined and compared. The resulting account is then related to Hunter and Thimm's epistemic approach to abstract probabilistic argumentation.

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.

There are a number of frameworks for modelling argumentation in logic. They incorporate formal representation of individual arguments and techniques for comparing conflicting arguments. In these frameworks, if there are a number of arguments for and against a particular conclusion, an aggregation function determines whether the conclusion is taken to hold. We propose a generalization of these frameworks. In particular, this new framework makes it possible to define aggregation functions that are sensitive to the number of arguments for or against(in most other frameworks, aggregation functions just consider the existence of arguments for and against). In this paper, we explore this framework (based on classical logic) in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item (which is a formula).

Modgil, Sanjay (King's College London) | Prakken, Henry (Utrecht University)

The ASPIC+ framework is intermediate in abstraction between Dung's argumentation framework and concrete instantiating logics. This paper generalises ASPIC+ to accommodate classical logic instantiations, and adopts a new proposal for evaluating extensions: attacks are used to define the notion of conflict-free sets, while the defeats obtained by applying preferences to attacks, are exclusively used to determine the acceptability of arguments. Key properties and rationality postulates are then shown to hold for the new framework.