Metainferential Duality

DA RÉ, BRUNO; TEIJEIRO, PAULA; SZMUC, DAMIÁN ENRIQUE; PAILOS, FEDERICO MATIAS

New York

Workshop; META-INFERENCES WORKSHOP; 2019

Saul Kripke Center at the GC-CUNY

The aim of this article is to discuss the extent to which certain substructural logics, and more generally some submetainferential logics, are related through the phenomenon of duality. Roughly speaking, metainferences are inferences between collections of inferences, and thus submetainferential logics can be regarded as those logics which have less valid metainferences than Classical Logic. In the spirit of kicking off the investigation of duality in substructural logics on an intuitive starting point, we will focus on the case study of the logics ST and TS, the former lacking Cut, the latter Reflexivity. The sense in which these logics, and these metainferences, are dual has never been made explicit in the context of a thorough and detailed exposition of duality for frameworks of this sort. Thus, our intent here is to try to elucidate whether or not this way of talking holds some ground---specially against the backdrop of the pool of notions of duality available in the specialized literature. In doing so, we hope to hint at broader points that might need to be addressed when studying duality in relation to substructural, and more generally with regard to submetainferential logics.