Determinism and looping in combinatory PDL
Theoretical Computer Science
An essay in combinatory dynamic logic
Information and Computation
Boosting the correspondence between description logics and propositional dynamic logics
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
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
The Description Logic Handbook
The Description Logic Handbook
On the undecidability of description and dynamic logics with recursion and counting
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Description Logics for Shape Analysis
SEFM '05 Proceedings of the Third IEEE International Conference on Software Engineering and Formal Methods
On the adaptive control of a class of SISO dynamic hybrid systems
Applied Numerical Mathematics
Reasoning within intuitionistic fuzzy rough description logics
Information Sciences: an International Journal
Reasoning within expressive fuzzy rough description logics
Fuzzy Sets and Systems
On the adaptive control of a class of SISO dynamic hybrid systems
Applied Numerical Mathematics
Enriched µ-calculi module checking
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Enriched µ-calculus pushdown module checking
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
The complexity of enriched µ-calculi
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Presburger modal logic is PSPACE-Complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Hi-index | 0.00 |
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 [Proc. IJCAR'01, in: Lecture Notes in Artif. Intel., vol. 2083, Springer, 2001, pp. 76-91] 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 improve a previous result [Proc. IJCAI'03, Morgan Kaufmann, 2003, pp. 331-336.] and prove that this calculus and the corresponding DL µACCIOfa are undecidable. We show also that nested fixpoints are not necessary for undecidability.