TY - GEN
T1 - A labelled sequent calculus for BBI
T2 - 22nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2013
AU - Hóu, Zhé
AU - Tiu, Alwen
AU - Goré, Rajeev
PY - 2013
Y1 - 2013
N2 - We present a labelled sequent calculus for Boolean BI (BBI), a classical variant of the logic of Bunched Implication. The calculus is simple, sound, complete, and enjoys cut-elimination. We show that all the structural rules in the calculus, i.e., those rules that manipulate labels and ternary relations, can be localised around applications of certain logical rules, thereby localising the handling of these rules in proof search. Based on this, we demonstrate a free variable calculus that deals with the structural rules lazily in a constraint system. We propose a heuristic method to quickly solve certain constraints, and show some experimental results to confirm that our approach is feasible for proof search. Additionally, we conjecture that different semantics for BBI and some axioms in concrete models can be captured by adding extra structural rules.
AB - We present a labelled sequent calculus for Boolean BI (BBI), a classical variant of the logic of Bunched Implication. The calculus is simple, sound, complete, and enjoys cut-elimination. We show that all the structural rules in the calculus, i.e., those rules that manipulate labels and ternary relations, can be localised around applications of certain logical rules, thereby localising the handling of these rules in proof search. Based on this, we demonstrate a free variable calculus that deals with the structural rules lazily in a constraint system. We propose a heuristic method to quickly solve certain constraints, and show some experimental results to confirm that our approach is feasible for proof search. Additionally, we conjecture that different semantics for BBI and some axioms in concrete models can be captured by adding extra structural rules.
UR - http://www.scopus.com/inward/record.url?scp=84885731803&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-40537-2_16
DO - 10.1007/978-3-642-40537-2_16
M3 - Conference contribution
SN - 9783642405365
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 172
EP - 178
BT - Automated Reasoning with Analytic Tableaux and Related Methods - 22nd International Conference, TABLEAUX 2013, Proceedings
Y2 - 16 September 2013 through 19 September 2013
ER -