Decision procedures and expressiveness in the temporal logic of branching time
Journal of Computer and System Sciences
Journal of the ACM (JACM)
Bisimulation through probabilistic testing
Information and Computation
CTL and ECTL as fragments of the modal &mgr;-calculus
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
The Complexity of Tree Automata and Logics of Programs
SIAM Journal on Computing
Completeness of Kozen's axiomatisation of the propositional &mgr;-calculus
Information and Computation
Alternating-time temporal logic
Journal of the ACM (JACM)
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Complete axiomatization and decidability of alternating-time temporal logic
Theoretical Computer Science
The Description Logic Handbook
The Description Logic Handbook
Semantical consideration on floyo-hoare logic
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
CoLoSS: The Coalgebraic Logic Satisfiability Solver
Electronic Notes in Theoretical Computer Science (ENTCS)
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
EXPTIME tableaux for the coalgebraic µ-calculus
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Cut elimination in coalgebraic logics
Information and Computation
Optimal tableau algorithms for coalgebraic logics
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
On monotone modalities and adjointness
Mathematical Structures in Computer Science
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Fixed point logics are widely used in computer science, in particular in artificial intelligence and concurrency. The most expressive logics of this type are the µ-calculus and its relatives. However, popular fixed point logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the µ-calculus. The family of such flat fixed point logics includes, e.g., CTL, the *-nesting-free fragment of PDL, and the logic of common knowledge. Here, we extend this notion to the generic semantic framework of coalgebraic logic, thus covering a wide range of logics beyond the standard µ-calculus including, e.g., flat fragments of the graded µ-calculus and the alternating-time µ-calculus (such as ATL), as well as probabilistic and monotone fixed point logics. Our main results are completeness of the Kozen-Park axiomatization and a timed-out tableaux method that matches EXPTIME upper bounds inherited from the coalgebraic µ-calculus but avoids using automata.