Logic and pragmatics: Linear logic for inferential practice

In this paper I discuss logic in the pragmatic approach of (Brandom, 2008). I consider different logical consequence relations (classical, intuitionistic and linear) and I will argue that the formal treatment proposed by Brandom, even if I believe it provides powerful intuitions and an interesting framework on logic in general, doesn't allow to state properly the relationship between different logics. I propose an alternative account of the elaboration of logical vocabularies not based on incompatibility semantics, rather on a particular notion of interaction, which I claim is implicit in the practice of giving and asking for reasons, which allows to state the relationship between different logics in terms of different aspects of the inferential practice.