A Sequent Calculus Perspective on Base-Extension Semantics

We define base-extension semantics ( $$\textsf{BeS}$$ BeS ) using atomic systems based on sequent calculus rather than natural deduction. While traditional $$\textsf{BeS}$$ BeS aligns naturally with intuitionistic logic due to its constructive foundations, we show that sequent calculi with multiple conclusions yield a $$\textsf{BeS}$$ BeS framework more suited to classical semantics. The harmony in classical sequents leads to straightforward semantic clauses derived solely from right introduction rules. This framework enables a Sandqvist-style completeness proof that extracts a sequent calculus proof from any valid semantic consequence. Moreover, we show that the inclusion or omission of atomic cut rules meaningfully affects the semantics, yet completeness holds in both cases.