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Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on\emph{proof} (as opposed to truth). There are two major approaches to P-tS:proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The formeris a semantics of arguments, and the latter is a semantics of logical constantsin a logic. This paper demonstrates that the B-eS for intuitionisticpropositional logic (IPL) encapsulates the declarative content of a basicversion of P-tV. Such relationships have been considered before yieldingincompleteness results. This paper diverges from these approaches by accountingfor the constructive, hypothetical setup of P-tV. It explicates how the B-eSfor IPL works.

From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic