ST’s Meta-Paracompleteness

Abstract

The logic ST [10] has been alternatively identified with classical logic due to its set of valid inferences, and with the logic LP, as demonstrated by Barrio et al. [7], through the ability to translate every valid metainference of ST into a valid inference of LP. Furthermore, [18] have argued that ST and LP are the same logic given their membership in the same equivalence class according to Blok-Jónsson’s theory of consequence. These two results connecting ST with LP have led to the perception of ST as a form of paraconsistent logic, at least metainferentially. In this work, a different characterization of the metainferences of ST is proposed through the inferences of the paracomplete logic K3, by arguing that this presentation is as legitimate as the other perspectives on this logic available in the literature. Utilizing new insights into the nature of the duality between the logics LP and K3 [as featured in 9], a translation from every valid metainference of ST into a valid inference of the logic K3 is offered. Additionally, a possible understanding of the notion of external logic is considered, allowing K3 to be viewed as the external logic of ST. Finally, an interpretation of the notion of consequence is presented that provides a natural understanding of the metainferences of ST as metainferential counterparts of the inferences of K3.