Completeness of atomic initial sequents

The concept of completeness in the context of atomic initial sequents is primarily discussed in the realm of formal logic and proof theory, particularly in relation to sequent calculi, which are systems used for representing logical deductions. **Atomic Initial Sequents** refer specifically to sequents that consist of atomic formulas only. A sequent generally has the form \( A_1, A_2, ..., A_n \vdash B \), where the formulas \( A_1, A_2, ...