An Adaptive Logic Based on Jaśkowski's Approach to Paraconsistency

In this paper, I present the modal adaptive logic$AJ^{r}$(based on S5) as well as the discussive logic$D_{2}^{r}$that is defined from it.$D_{2}^{r}$is a (nonmonotonic) alternative for Jaśkowski's paraconsistent system D₂. Like D₂,$D_{2}^{r}$validates all single-premise rules of Classical Logic. However, for formulas that behave consistently,$D_{2}^{r}$moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D₂, this does not require the introduction of discussive connectives. It is argued that this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions.