Studia Logica 107 (1):233-246 (2019)

Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, satisfy at least one of these conditions, thus rendering IPC semantically incomplete for them. Only for Goldfarb’s [1] proof-theoretic semantics, which deviates from standard approaches, IPC turns out to be complete. Overall, these results show that basic ideas of proof-theoretic semantics for propositional logic are not captured by IPC.
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DOI 10.1007/s11225-018-9823-7
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References found in this work BETA

Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
Concerning Formulas of the Types a →B ∨C, a →(Ex)B(X).Ronald Harrop - 1960 - Journal of Symbolic Logic 25 (1):27-32.

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Proof-Theoretic Semantics and Inquisitive Logic.Will Stafford - 2021 - Journal of Philosophical Logic 50 (5):1199-1229.

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