Generalized abstract argumentation: A first-order machinery towards ontology debugging

Abstract

Same as Dung's abstract argumentation framework (AF), the notion of generalized abstract argumentation framework (GenAF) aims at reasoning about inconsistency disregarding any logic for arguments; thus both the knowledge base (KB) and language to express beliefs remain unspecified. Nonetheless, reifying the abstract configuration of the AF argumentation machineries to specific logics may bring about some inconveniences. A GenAF is assumed to eventually relate first-order logic (FOL) formulae to abstract arguments. The main purpose of the generalization is to provide a theory capable of reasoning (following argumentation technics) about inconsistent knowledge bases (KB) expressed in any FOL fragment. Consequently, the notion of argument is related to a single formula in the KB. This allows to share the same primitive elements from both, the framework (arguments) and, the KB (formulae). A framework with such features would not only allow to manage a wide range of knowledge representation languages, but also to cope straightforwardly with the dynamics of knowledge. Once the formalism is presented, we propose a reification to the description logic ALC with the intention to handle ontology debugging. In this sense, since argumentation frameworks reason over graphs that relate arguments through attack, our methodology is proposed to bridge ontological inconsistency sources to attack relations in argumentation. Finally, an argumentation semantics adapted to GenAF's, is proposed as a consistency restoration tool with the objective of debugging and repairing ontologies. © AEPIA and the authors.