Basic proof theory
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
STRIP: Structural Sharing for Efficient Proof-Search
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Two Loop Detection Mechanisms: A Comparision
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic
Journal of Logic and Computation
A decidable constructive description logic
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
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In this paper we present LSJ, a contraction-free sequent calculus for Intuitionistic propositional logic whose proofs are linearly bounded in the length of the formula to be proved and satisfy the subformula property. We also introduce a sequent calculus RJ for intuitionistic unprovability with the same properties of LSJ. We show that from a refutation of RJ of a sequent 驴 we can extract a Kripke counter-model for 驴. Finally, we provide a procedure that given a sequent 驴 returns either a proof of 驴 in LSJ or a refutation in RJ such that the extracted counter-model is of minimal depth.