We develop an incremental tableau-based decision procedure for the alternating-time temporal logic ATL and some of its variants. While running within the theoretically established complexity upper bound, we believe that our tableaux are practically more efficient in the average case than other decision procedures for ATL known so far. Besides, the ease of its adaptation to variants of ATL demonstrates the flexibility of the proposed procedure.
Goranko, V., & Shkatov, D. (2010). Tableau-Based Decision Procedures for Logics of Strategic Ability in Multiagent Systems. ACM Transactions on Computational Logic, 11(1), 3. https://doi.org/10.1145/1614431.1614434