A Pragmatic Interpretation Of Substructural Logics

Following work by Dalla Pozza and Garola on a pragmatic interpretation of intuitionistic and deontic logics, we present a sequent calculus ILP formalizing the derivation of assertive judgements and obligations from mixed contexts of assertions, obligations and expressions of the causal interactions between them. To express a notion of causal implication, the sequents of ILP have two areas expressing the relevant and the ordinary intuitionistic consequence relations, respectively. Moreover we consider a "free logic of pragmatic force" where illocutionary operators are unspecified and argue the consequence relation for such a logic must be indeed linear. It is also argued that the above uses of relevant and linear logic are philosophically compatible with a theory of pragmatics in a classic semantical setting and immune from confusions about intuitive interpretations of substructural logics.