Three questions on Jaśkowski’s discussive logic

Hitoshi Omori

Stanisław Jaśkowski is known to be one of the modern founders of paraconsistent logic, together with Newton C. A. da Costa. The most important contribution of Jaśkowski is that he clearly distinguished two notions for a theory, namely a theory being contradictory (or inconsistent) and a theory being trivial (or overfilled). In addition to this distinction, he also presented a system of paraconsistent logic known as D2 which is often referred to as discursive logic or discussive logic. Very briefly put, D2 was introduced via modal logic S5, building on a certain idea related to discussion, and seen as a typical non-adjunctive system of paraconsistent logic.

The aim of this talk is to address the following three questions:

(i) Are there other modal logics than S5 that will be sufficient to define D2?
(ii) Are there other ways to capture Jaśkowski’s idea than the well-known translation?
(iii) Is there more to discussive logic than being non-adjunctive?

These questions are, of course, not entirely new. In particular, the first question has led to a number of interesting and non-trivial results. However, there seem to be other answers than those already discussed in the literature, and I will present some new answers to the above questions.

(The results related to the first and the second questions build on joint work with Fabio De Martin Polo and Igor Sedlár, respectively.)