The original sin of proof-theoretic semantics

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims atexplaining the meaning of the logical constants in terms of the i nference rules thatgovern their behaviour in proofs. We argue that this must be construed as the task ofexplaining these meanings relative to a logic, i.e., to a consequence relation.Alas,there is no agreed set of properties that a relation must have in order to qualify as aconsequence relation. Moreover, the association of a consequence relation to a logicalcalculus is not as straightforward as it may seem. We show that these facts are prob-lematic for the proof-theoretic project but the problems can be solved. Our thesis isthat the consequence relation relevant for proof-theoretic semantics is the one givenby the sequent-to-sequent derivability relation in Gentzen systems.