“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Combining deduction and model checking into Tableaux and algorithms for converse-PDL
Information and Computation
Modal logic
Dynamic Logic
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A Tableau Decision Procedure for $\mathcal{SHOIQ}$
Journal of Automated Reasoning
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Terminating Tableaux for Hybrid Logic with the Difference Modality and Converse
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
An On-the-fly Tableau-based Decision Procedure for PDL-satisfiability
Electronic Notes in Theoretical Computer Science (ENTCS)
Terminating Tableau Systems for Hybrid Logic with Difference and Converse
Journal of Logic, Language and Information
An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Clausal graph tableaux for hybrid logic with eventualities and difference
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Correctness and worst-case optimality of Pratt-style decision procedures for modal and hybrid logics
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Clausal Tableaux for Hybrid PDL
Electronic Notes in Theoretical Computer Science (ENTCS)
Constructive formalization of hybrid logic with eventualities
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
A Goal-Directed Decision Procedure for Hybrid PDL
Journal of Automated Reasoning
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We present the first terminating tableau system for hybrid logic with eventualities. The system is designed as a basis for gracefully degrading reasoners. Eventualities are formulas of the form $\Diamond^*s$ that hold for a state if it can reach in n≥0 steps a state satisfying the formula s. The system is prefix-free and employs a novel clausal form that abstracts away from propositional reasoning. It comes with an elegant correctness proof. We discuss some optimizations for decision procedures.