Metainferential Constants

PAILOS, FEDERICO MATÍAS; RUBIN, MARIELA

Workshop; X Workshop on Philosophical Logic; 2021

IIF-SADAF

A metainference is usually understood as a pair consisting of a set of inferences, called premises, and a single inference, called conclusion. In the last few years, much attention has been paid to the study of metainferences ?in particular, to the question of what are the valid metainferences in a given logic. So far, however, this study has been done in a quite poor language. Our usual formal apparatus have no way to represent, e.g. negated inferences, a disjunction in the premises of a metainference or a conjunction in the conclusion. In this paper we tackle these expressive issues. We define an inferential language?a language whose atomic formulas are inferences. We provide a semantic characterisation of validity for this language. We argue that our inferential language is interesting for its expressiveness. In particular, it enables forms of metainferences not yet analysed in the literature, and it allows for a better understanding of the sense in which many known non-classical logics have a classical metatheory. Barrio et al. 2016 proved that the valid metainferences of logic ST correspond to the valid inferences of logic LP. We show that this result remains true in our inferential language. Also, we prove that an analogous result holds for logics TS and K3. We provide sound complete proof systems for logics CL, LP, K3, ST and TS in our inferential language. Finally, we extend this framework to every higher (finite) metainferential level. This is a joint work with Camillo Fiore.