Handbook of logic in artificial intelligence and logic programming (vol. 1)
Relational formalisation of nonclassical logics
Relational methods in computer science
Strongly Analytic Tableaux for Normal Modal Logics
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Tableaux and Algorithms for Propositional Dynamic Logic with Converse
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Tableaux Based Decision Procedures for Modal Logics of Confluence and Density
Fundamenta Informaticae
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In this paper we generalize the existing tableau methods for modal logics. First of all, while usual modal tableaux are based on trees, our basic structures are rooted directed acyclic graphs (RDAG). This allows natural tableau rules for some modal logics that are difficult to capture in the usual way (such as those having an accessibility relation that is dense or confluent). Second, tableau rules rewrite patterns, which are (schemas of) parts of a RDAG. A particular case of these rules are the single-step rules recently proposed by Massacci. This allows in particular tableau rule presentations for K5, KD5, K45, KD45, and S5 that respect the subformula property. Third, we divide modal tableau rules into propagation rules and structural rules. Structural rules construct new edges and nodes (without adding formulas to nodes), while propagation rules add formulas to nodes. This distinction allows to prove completeness in a modular way.