Belief selection through argumentation.

Dung's argumentation framework proved to be a powerful framework for reasoning about inconsistent beliefs. We revisit preference-based argumentation frameworks (PAF) for handling inconsistent beliefs encoded in classical propositional logic. We first define rational properties that should be fulfilled by the defeat relation. They are based on inconsistency and entailment. Then, using these two notions as a common thread we define three families of defeats between arguments, and two families of preference relations. We show that PAF with entailment-based preference relations satisfy interesting properties that are not satisfied by PAF with a general preference relation. Lastly, we apply our framework in datamining pattern selection.