Modal tableaux with propagation rules and structural rules
Fundamenta Informaticae
Modal logic
Dynamic Logic
Using tableau to decide expressive description logics with role negation
ISWC'07/ASWC'07 Proceedings of the 6th international The semantic web and 2nd Asian conference on Asian semantic web conference
Automated Synthesis of Tableau Calculi
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A description logic based situation calculus
Annals of Mathematics and Artificial Intelligence
Tableau calculi for CSL over minspaces
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Synthesising terminating tableau calculi for relational logics
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Using tableau to decide description logics with full role negation and identity
ACM Transactions on Computational Logic (TOCL)
A Goal-Directed Decision Procedure for Hybrid PDL
Journal of Automated Reasoning
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This paper presents a general method for proving termination of tableaux-based procedures for modal-type logics and related first-order fragments. The method is based on connections between filtration arguments and tableau blocking techniques. The method provides a general framework for developing tableau-based decision procedures for a large class of logics. In particular, the method can be applied to many well-known description and modal logics. The class includes traditional modal logics such as S4and modal logics with the universal modality, as well as description logics such as $\mathcal{ALC}$ with nominals and general TBoxes. Also contained in the class are harder and less well-studied modal logics with complex modalities and description logics with complex role operators such as Boolean modal logic, and the description logic $\mathcal{ALBO}$. In addition, the techniques allow us to specify tableau-based decision procedures for related solvable fragments of first-order logic, including the two-variable fragment of first-order logic.