Focused Proof-search in the Logic of Bunched Implications

Abstract The logic of Bunched Implications (BI) freely combines additive and multiplicative connectives, including implications; however, despite its well-studied proof theory, proof-search in BI has always been a difficult problem. focusing principle is restriction the space that can capture various goal-directed procedures. In this paper we show focused complete for by first reformulating traditional bunched sequent calculus using simpler data-structure nested sequents, following with polarised variant sound via cut-elimination argument. This establishes an operational semantics Implications.