Intensionality of consequence and identity of proofs in Prawitz’s Theory of Grounds

I discuss two possible ways for dealing with a constructive, proof based notion of logical consequence. The first, qualified as extensional, amounts to the idea that a given proof-structure is justifiable under every interpretation of the non-logical terminology it involves. The second, qualified as intensional, requires on the contrary that the given proof-structure be justified independently of its non-logical meaning. Contrarily to the extensional approach, the intensional account calls for a prior treatment of the notion of identity of proofs. Identity can be in turn addressed in an extensional or intensional way. Although these issues are obviously of a more general interest, I investigate them in a framework which seems to me to be particularly well-suited for the purpose, i.e., Prawitz’s (non-monotonic) Theory of Grounds.