Bruno Da Ré and Federico Pailos: “Sequent-calculi for metainferential logics”
In recent years, some theorists have argued that the logics are not only defined by their inferences, but also by their metainferences. In this sense, logics which coincide in their inferences, but not in their metainferences were considered to be different logics. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as ST, LP, K3 and TS. What is distinctive of these metainferential logics is that they are mixed, i.e. the standard for the premises and for the conclusion is not necessarily the same. However, so far, all of these systems have been presented following a semantical standpoint, in terms of valuations based on the Strong Kleene matrices. In this article, we provide sound and complete sequent-calculi for the valid inferences and the invalid inferences of the logics ST, LP ,K3 and TS, and introduce an algorithm that allows to obtain sound and complete sequent-calculi for the validities and the invalidities of any metainferential logic of any level.