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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. [ABSTRACT FROM AUTHOR]

After reviewing the basic definitions of harmony and stability, two of the central concepts in Proof-Theoretic Semantics, the paper considers the implicational fragment of the relevant logic R (Anderson&Belnap), under a labelled natural deduction (ND) system, where the labels keep track of 'use' of assumptions. Thereby, no assumption is discharged that has not been used. It is shown that the ND is not closed under composition of derivations using its standard definition, thereby prohibiting Prawitz's detour removal reductions, hence failing harmony.Arevised definition of derivation composition is proposed, under which the ND system *is* closed, allowing reductions and reenabling harmony (and stability). [ABSTRACT FROM AUTHOR]