Tableau Calculi for the Logics of Finite k-Ary Trees

Authors:
Mauro Ferrari;Camillo Fiorentini;Guido Fiorino
Affiliations:
-;-;-
Venue:
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Year:
2002

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Abstract

We present tableau calculi for the logics Dk (k 驴 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 Dk, in particular their constructivity and their decidability.