Abstract
We present tableau calculi for the logics D k (k≥2) semantically characterized by the classes of Kripke models built on finite k-ary trees. Our tableau calculi use the signs T and F, some tableau rules for Intuitionistic Logic and two rules formulated in a hypertableau fashion. We prove the Soundness and Completeness Theorems for our calculi. Finally, we use them to prove the main properties of the logics D k, in particular their constructivity and their decidability.
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Ferrari, M., Fiorentini, C., Fiorino, G. (2002). Tableau Calculi for the Logics of Finite k-Ary Trees. In: Egly, U., Fermüller, C.G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2002. Lecture Notes in Computer Science(), vol 2381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45616-3_9
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DOI: https://doi.org/10.1007/3-540-45616-3_9
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