Calcul d'arguments et de contre-arguments fondé sur les noyaux inconsistants

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 Set). The idea relies on the fact that reduction ad absurdum is valid in propositional logic: (φ, ψ) is an argument induced from a knowledge base δ iff φ [{¬ψ} is minimal inconsistent. Therefore, if φ [{¬ψ} is a MUS of δU [{¬ψ} that contains at least one clause of ¬ψ then (φ, ψ) 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.