Views of proof-theoretic semantics: reified proof-theoretic meanings

The paper surveys several views of proof-theoretic semantics and classifies them in accordance to the choice of which of the rules of a meaning-conferring natural-deduction system determines the meaning of the defined expression. Then, in contrast to the traditional approach that regards the rules as determining meaning implicitly, the paper proposes an explicit definition of meaning in terms of rules, appealing to collections of canonical derivations. A certain claim about a conclusion from the non-eliminability of the rules that are not meaning conferring is refuted, and an alternative explanation of non-eliminability is proposed.