Strong Equivalence for Argumentation Frameworks with Collective Attacks

Abstract

Dung´s abstract argumentation frameworks (AFs) are a popular conceptual tool to define semantics for advanced argumentation formalisms. Hereby, arguments representing a possible inference of a claim are constructed and an attack relation between arguments indicates certain conflicts between the claim of one argument and the inference of another. Based on this abstract model, sets of jointly acceptable arguments are then gathered and finally interpreted in terms of their claims. Argumentation formalisms following this type of instantiating Dung AFs naturally produce several arguments with the same claim. This causes several issues and challenges for argumentation systems: on the one hand, the relation between claims remains implicit and, on the other hand, determining the acceptance of claims requires additional computations on top of argument acceptance. An instantiation that avoids this situation could provide additional insights and advantages, thus complementing the standard instantiation process via Dung AFs. Consequently, the research question we tackle is as follows: Can one combine different arguments sharing the same claim to a single abstract argument without affecting the overall results (and which abstract formalisms can serve such a purpose)? As a main result we show that a certain class of frameworks, where arguments with the same claim have the same outgoing attacks, can be equivalently (for all standard semantics) represented as argumentation frameworks with collective attacks where each claim occurs in exactly one argument. We further identify a class of frameworks where one even obtains an equivalent Dung AF with just one argument per claim.