Argumentative Logics: Reasoning with Classically Inconsistent Information

Classical logic has many appealing features for knowledge representation and reasoning. But unfortunately it is awed when reasoning about inconsistent information, since anything follows from a classical inconsistency. This problem is addressed by introducing the notions of \argument" and of \acceptability" of an argument. These notions are used to introduce the concept of \argumentative structures". Each deenition of acceptability selects a subset of the set of arguments, and an argumentative structure is a subset of the power set of arguments. In this paper, we consider, in detail , a particular argumentative structure, where each argument is deened as a classical inference together with the applied premisses. For such arguments , a variety of deenitions of acceptability are provided, the properties of these deenitions are explored, and their interrelationship described. The deenitions of acceptability induce a family of logics called argumentative logics which we explore. The relevance of this work is considered and put in a wider perspective.