MUS-based generation of arguments and counter-arguments

Most of the approaches of computational argumentation define an argument as a pair consisting of premises and a conclusion, where the latter is entailed by the former. However, the matter of computing arguments and counter-arguments remains largely unsettled. We propose here a method to compute arguments and counter-arguments in the context of propositional logic, by using the concept of a MUS (Minimally Unsatisfiable Subset). The idea relies on the fact that reduction ad absurdum is valid in propositional logic: (Φ, α) is an argument induced from a knowledge base Δ iff Φ∪ {¬α} is inconsistent. Therefore, if Φ∪ { ¬α} is a MUS of Δ∪ {¬α} that contains :¬α then (Φ, α) is an argument from Δ. Not only do we present an algorithm that generates arguments, we also present an algorithm generating the complete argumentation tree induced by a given argument. We include a report on computational experimentations with both algorithms.