Argumentation-Based Proof Procedures for Credulous and Sceptical Non-monotonic Reasoning

We define abstract proof procedures for performing credulous and sceptical non-monotonic reasoning, with respect to the argumentation-theoretic formulation of non-monotonic reasoning proposed in [1]. Appropriate instances of the proposed proof procedures provide concrete proof procedures for concrete formalisms for non-monotonic reasoning, for example logic programming with negation as failure and default logic. We propose (credulous and sceptical) proof procedures under different argumentation-theoretic semantics, namely the conventional stable model semantics and the more liberal partial stable model or preferred extension semantics. We study the relationships between proof procedures for different semantics, and argue that, in many meaningful cases, the (simpler) proof procedures for reasoning under the preferred extension semantics can be used as sound and complete procedures for reasoning under the stable model semantics. In many meaningful cases still, proof procedures for credulous reasoning under the preferred extension semantics can be used as (much simpler) sound and complete procedures for sceptical reasoning under the preferred extension semantics. We compare the proposed proof procedures with existing proof procedures in the literature.