Abstract Argumentation Frameworks with Domain Assignments

Argumentative discourse rarely consists of opinions whose claims apply universally. As with logical statements, an argument applies to specific objects in the universe or relations among them, and may have exceptions. In this paper, we propose an argumentation formalism that allows associating arguments with a domain of application. Appropriate semantics are given, which formalise the notion of partial argument acceptance, i.e., the set of objects or relations that an argument can be applied to. We show that our proposal is in fact equivalent to the standard Argumentation Frameworks of Dung, but allows a more intuitive and compact expression of some core concepts of commonsense and non-monotonic reasoning, such as the scope of an argument, exceptions, relevance and others

Theoretical Analysis and Implementation of Abstract Argumentation Frameworks with Domain Assignments

A representational limitation of current argumentation frameworks is their inability to deal with sets of entities and their properties, for example to express that an argument is applicable for a specific set of entities that have a certain property and not applicable for all the others. In order to address this limitation, we recently introduced Abstract Argumentation Frameworks with Domain Assignments (AAFDs), which extend Abstract Argumentation Frameworks (AAFs) by assigning to each argument a domain of application, i.e., a set of entities for which the argument is believed to apply. We provided formal definitions of AAFDs and their semantics, showed with examples how this model can support various features of commonsense and non-monotonic reasoning, and studied its relation to AAFs. In this paper, aiming to provide a deeper insight into this new model, we present more results on the relation between AAFDs and AAFs and the properties of the AAFD semantics, and we introduce an alternative, more expressive way to define the domains of arguments using logical predicates. We also offer an implementation of AAFDs based on Answer Set Programming (ASP) and evaluate it using a range of experiments with synthetic datasets