Efficient Loop-Check for Backward Proof Search in Some Non-classical Propositional Logics
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Analyzing the Core of Categorial Grammar
Journal of Logic, Language and Information
A Formulae-as-Types Interpretation of Subtractive Logic
Journal of Logic and Computation
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic
Journal of Logic and Computation
A local system for intuitionistic logic
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A connection-based characterization of bi-intuitionistic validity
CADE'11 Proceedings of the 23rd international conference on Automated deduction
BDD-based automated reasoning for propositional bi-intuitionistic tense logics
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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Bi-intuitionistic logic is the extension of intuitionistic logic with exclusion, a connective dual to implication. Cut-elimination in bi-intuitionistic logic is complicated due to the interaction between these two connectives, and various extended sequent calculi, including a display calculus, have been proposed to address this problem. In this paper, we present a new extended sequent calculus DBiInt for bi-intuitionistic logic which uses nested sequents and "deep inference", i.e., inference rules can be applied at any level in the nested sequent. We show that DBiInt can simulate our previous "shallow" sequent calculus LBiInt. In particular, we show that deep inference can simulate the residuation rules in the display-like shallow calculus LBiInt. We also consider proof search and give a simple restriction of DBiInt which allows terminating proof search. Thus our work is another step towards addressing the broader problem of proof search in display logic.