Alternating-time temporal logic
Journal of the ACM (JACM)
MOCHA: Modularity in Model Checking
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Two-variable logic with counting is decidable
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Alternating-time temporal logics with irrevocable strategies
TARK '07 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge
CTL Model-Checking with Graded Quantifiers
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
ATL with Strategy Contexts and Bounded Memory
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Graded-CTL: Satisfiability and Symbolic Model Checking
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
A NuSMV extension for Graded-CTL model checking
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
MCMAS: a model checker for multi-agent systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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Graded modalities enrich the universal and existential quantifiers with the capability to express the concept of at least k or all but k, for a non-negative integer k. Recently, temporal logics such as µ-calculus and Computational Tree Logic, Ctl, augmented with graded modalities have received attention from the scientific community, both from a theoretical side and from an applicative perspective. Both µ-calculus and Ctl naturally apply as specification languages for closed systems: in this paper, we add graded modalities to the Alternating-time Temporal Logic (Atl) introduced by Alur et al., to study how these modalities may affect specification languages for open systems. We present, and compare with each other, three different semantics. We first consider a natural interpretation which seems suitable to off-line synthesis applications and then we restrict it to the case where players can only employ memoryless strategies. Finally, we strengthen the logic by means of a different interpretation which may find application in the verification of fault-tolerant controllers. For all the interpretations, we efficiently solve the model-checking problem both in the concurrent and turn-based settings, proving its PTIME-completeness. To this aim we also exploit also a characterization of the maximum grading value of a given formula.