Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very powerful, subsuming all major previously studied modal logics for strategic reasoning, including ATL, ATL*, and the like. Unfortunately, due to its high expressiveness, SL has a non-elementarily decidable model-checking problem and the satisfiability question is undecidable, specifically Sigma_1^1. In order to obtain a decidable sublogic, we introduce and study here One-Goal Strategy Logic (SL[1G], for short). This is a syntactic fragment of SL, strictly subsuming ATL*, which encompasses formulas in prenex normal form having a single temporal goal at a time, for every strategy quantification of agents. We prove that, unlike SL, SL[1G] has the bounded tree-model property and its satisfiability problem is decidable in 2ExpTime, thus not harder than the one for ATL*.Comment: arXiv admin note: text overlap with arXiv:1112.6275, arXiv:1202.1309

@article{MogaveroMPV16,
  title = {Reasoning about Strategies: on the Satisfiability Problem},
  author = {Fabio Mogavero and Aniello Murano and Giuseppe Perelli and Moshe Y. Vardi},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 13, Issue 1},
  year = {2017},
  doi = {10.23638/lmcs-13(1:9)2017}
}