Towards Service Description Logics
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Reasoning in Expressive Description Logics with Fixpoints based on Automata on Infinite Trees
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
On the undecidability of logics with converse, nominals, recursion and counting
Artificial Intelligence
On the decidability of containment of recursive datalog queries - preliminary report
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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The evolution of Description Logics (DLs) and Propositional Dynamic Logics produced a hierarchy of decidable logics with multiple maximal elements. It would be desirable to combine different maximal logics into one super-logic, but then inference may turn out to be undecidable. Then it is important to characterize the decidability threshold for these logics. In this perspective, an interesting open question pointed out by Sattler and Vardi [Sattler and Vardi, 1999] is whether inference in a hybrid µ-calculus with restricted forms of graded modalities is decidable, and which complexity class it belongs to. In this paper we prove that this calculus and the corresponding DL µALCIOf are undecidable. Second, we prove undecidability results for logics that support both a transitive closure operator over roles and number restrictions.