Pragmatic connectives as predicates : the case of inferential connectives

This chapter investigates the linguistic description and formal representation of some pragmatic inferential connectives in French. We show that connectives expressing consequence, oppposition or reformulation presuppose an abstract relation between propositional arguments of certain semantic types. We first contrast inferential and non-inferential vonnectives, then we turn to the semantic types of the propositional arguments to lay down some basic distinctions. Finally we substantiate the relations themselves. We use a version of generalized quantification over proofs to describe the inferential constraints which define the various relations presupposed by the connectives. The very possibility of such a description suggests that inferential connectives have a genuine (presupposed) predicative content