A generalized abstract argumentation framework for inconsistency-tolerant ontology reasoning

We propose a new family of abstract argumentation frameworks which we refer to as generalized (identified through the acronym GenAF), due to its ability of adapting to different representation languages. GenAFs are formalized upon an unspecified representation language L but enriched with some inner structure which allows relating formulæ from the underlying knowledge base with primitive elements of arguments. The well-known Dung's standard semantics are adapted to construct the GenAF's reasoning machinery. As an application, we reify the GenAF's abstract language for arguments with the basic ALC flexibility of the presented formalism and a way of applying argumentation for reasoning over inconsistent ontologies. Finally, a detailed study is performed on the matter of argumentation rationality. The GenAF when concretized into a generalized argumentation system (GenAS) is studied under specific conditions which turn it into a standard logic-based argumentation system. This brings the opportunity to verify the scope of widely accepted postulates for logic-based argumentation to control the well behavior of the GenAS and to relate it to other argumentation systems.