Closure and Consistency Rationalities in Logic-Based Argumentation

Caminada and Amgoud have argued that logic-based argumentation systems should satisfy the intuitive and natural principles of logical closure and consistency. Prakken has developed this idea further for a richer logic. A question arises naturally whether a general structure guaranteeing the logical closure and consistency properties could be identified that is common for all underlying logics. We explore this question by first defining a logic-based argumentation framework as combination of an abstract argumentation framework with a monotonic Tarski-like consequence operator. We then demonstrate that the logical closure and consistency properties are rested on a simple notion of a base of arguments from which the argument could be constructed in an indefeasible way (using the monotonic consequence operator) and the only way to attack an argument is to attack its base. We show that two natural properties of structural closure and consistency covering based on the idea of bases of arguments indeed guarantee the logical closure and consistency properties. We demonstrate how the properties of structural closure and consistency covering are captured naturally in argumentation systems of Caminada, Amgoud and Prakken as well as in assumption-based argumentation.