Revisiting argumentation in light of squares of oppositions

Formal AI models of argumentation define arguments as reasons that support claims. Such arguments may be attacked by other arguments. The main issue is then to identify the accepted ones. Works in linguistics rather focus on understanding the notion of argument, identifying its types, and describing different forms of counter-argumentation. This paper advocates that such typologies are instrumental for capturing real argumentations. It shows that some of the forms cannot be handled properly by AI models. Finally, it shows that the use of square of oppositions (a very old logical device) illuminates the interrelations between the different forms of argumentation.