Starting from a typology of argumentative forms proposed in linguistics by Apothéloz, and observing that the four basic forms can be organized in a square of oppositions, we present a logical language, somewhat inspired from generalized possibilistic logic, where these basic forms can be expressed. We further analyze the interplay between the formulas of this language by means of two hexagons of oppositions. We then outline the inference machinery underlying this logic, and discuss its interest for argumentation.