Abstract
We present Gbu, a terminating variant of the sequent calculus G3i for intuitionistic propositional logic. Gbu modifies G3i by annotating the sequents so to distinguish rule applications into two phases: an unblocked phase where any rule can be backward applied, and a blocked phase where only right rules can be used. Derivations of Gbu have a trivial translation into G3i. Rules for right implication exploit an evaluation relation, defined on sequents; this is the key tool to avoid the generation of branches of infinite length in proof-search. To prove the completeness of Gbu, we introduce a refutation calculus Rbu for unprovability dual to Gbu. We provide a proof-search procedure that, given a sequent as input, returns either a Rbu-derivation or a Gbu-derivation of it.
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References
Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford University Press (1997)
Dyckhoff, R., Lengrand, S.: LJQ: A Strongly Focused Calculus for Intuitionistic Logic. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol. 3988, pp. 173–185. Springer, Heidelberg (2006)
Ferrari, M., Fiorentini, C., Fiorino, G.: Contraction-free linear depth sequent calculi for intuitionistic propositional logic with the subformula property and minimal depth counter-models. Journal of Automated Reasoning 51(2), 129–149 (2013)
Ferrari, M., Fiorentini, C., Fiorino, G.: Simplification rules for intuitionistic propositional tableaux. ACM Transactions on Computational Logic (TOCL) 13(2), 14:1–14:23 (2012)
Gabbay, D.M., Olivetti, N.: Goal-Directed Proof Theory. Springer (2000)
Heuerding, A., Seyfried, M., Zimmermann, H.: Efficient loop-check for backward proof search in some non-classical propositional logics. In: Miglioli, P., Moscato, U., Ornaghi, M., Mundici, D. (eds.) TABLEAUX 1996. LNCS, vol. 1071, pp. 210–225. Springer, Heidelberg (1996)
Howe, J.M.: Two loop detection mechanisms: A comparision. In: Galmiche, D. (ed.) TABLEAUX 1997. LNCS, vol. 1227, pp. 188–200. Springer, Heidelberg (1997)
Massacci, F.: Simplification: A general constraint propagation technique for propositional and modal tableaux. In: de Swart, H. (ed.) TABLEAUX 1998. LNCS (LNAI), vol. 1397, pp. 217–231. Springer, Heidelberg (1998)
Pinto, L., Dyckhoff, R.: Loop-free construction of counter-models for intuitionistic propositional logic. In: Behara, M., et al. (eds.) Symposia Gaussiana, Conference A, pp. 225–232. Walter de Gruyter, Berlin (1995)
Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge Tracts in Theoretical Computer Science, vol. 43. Cambridge University Press (1996)
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Ferrari, M., Fiorentini, C., Fiorino, G. (2013). A Terminating Evaluation-Driven Variant of G3i. In: Galmiche, D., Larchey-Wendling, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2013. Lecture Notes in Computer Science(), vol 8123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40537-2_11
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DOI: https://doi.org/10.1007/978-3-642-40537-2_11
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