Simple contrapositive assumption-based argumentation frameworks with preferences: Partial orders and collective attacks

In this paper, we consider assumption-based argumentation frameworks that are based on contrapositive logics and partially-ordered preference functions. It is shown that these structures provide a general and solid platform for representing and reasoning with conflicting and prioritized arguments. Two useful properties of the preference functions are identified (selectivity and max-lower-boundedness), and extended forms of attack relations are supported (∃–attacks and ∀-attacks), which assure several desirable properties and a variety of formal settings for argumentation-based conclusion drawing. These two variations of attacks may be further extended to collective attacks. Such (existential or universal) collective attacks allow to challenge a collective of assertions rather than single assertions. We show that these extensions not only enhance the expressive power of the framework, but in certain cases also enable more rational patterns of reasoning with conflicting assertions.