Being a pragmatic and not a referential approach to semantics, the dialogical formulation of paraconsistency allows the following semantic idea to be expressed within a semi-formal system: In an argumentation it sometimes makes sense to distinguish between the contradiction of one of the argumentation partners with himself (internal contradiction) and the contradiction between the partners (external contradiction). The idea is that external contradiction may involve different semantic contexts in which, say A and not A have been asserted. The dialogical approach suggests a way of studying the dynamic process of contradictions through which the two contexts evolve for the sake of argumentation into one system containing both contexts. More technically, we show a new, dialogical, way to build paraconsistent systems for propositional and ﬁrst-order logic with classical and intuitionistic features (i.e. paraconsistency both with and without tertium non-datur) and present their corresponding tableaux.
Comment: This paper would fit well in a course on dialogical formulations of logic (as either main or further reading, depending on the time dedicated to Lorenz-style approaches), or in a course on paraconsistent logic (as an alternative way of thinking about paraconsistency); both topics are introduced in an accessible enough way. If students have no familiarity with tableaux systems, sections 4 and 5.2 can be skipped.