Sequent calculi for metainferential logics

DA RÉ, BRUNO; PAILOS, FEDERICO MATÍAS

STUDIA LOGICA

Springer

Año: 2021

0039-3215

In recent years, some theorists have argued that the logics are not only defined by theirinferences, but also by their metainferences. In this sense, logics that coincide in theirinferences, but not in their metainferences were considered to be different. 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 distinctiveof these metainferential logics is that they are mixed, i.e. the standard for the premisesand the conclusion is not necessarily the same. However, so far, all of these systems havebeen presented following a semantical standpoint, in terms of valuations based on theStrong Kleene truth-tables. In this article, we provide sound and complete sequent-calculifor the valid inferences and the invalid inferences of the logics ST, LP, K3 and TS, andintroduce an algorithm that allows obtaining sound and complete sequent-calculi for theglobal validities and the global invalidities of any metainferential logic of any level.