Mogavero, FabioMurano, AnielloVardi, Moshe Y.2013-06-282013-12-292014Mogavero, Fabio, Murano, Aniello and Vardi, Moshe Y.. "Relentful Strategic Reasoning in 1 Alternating-Time Temporal Logic." <i>Journal of Logic and Computation,</i> (2014) Oxford University Press: http://dx.doi.org/10.1093/logcom/exu052.https://hdl.handle.net/1911/71490Temporal logics are a well investigated formalism for the specification, verification, and synthesis of reactive systems. Within this family, Alternating-Time Temporal Logic (ATL , for short) has been introduced as a useful generalization of classical linear- and branching-time temporal logics, by allowing temporal operators to be indexed by coalitions of agents. Classically, temporal logics are memoryless: once a path in the computation tree is quantified at a given node, the computation that has led to that node is forgotten. Recently, mCTL has been defined as a memoryful variant of CTL , where path quantification is memoryful. In the context of multi-agent planning, memoryful quantification enables agents to “relent” and change their goals and strategies depending on their history. In this paper, we define mATL , a memoryful extension of ATL , in which a formula is satisfied at a certain node of a path by taking into account both the future and the past. We study the expressive power of mATL , its succinctness, as well as related decision problems. We also investigate the relationship between memoryful quantification and past modalities and show their equivalence. We show that both the memoryful and the past extensions come without any computational price; indeed, we prove that both the satisfiability and the model-checking problems are 2EXPTIME-COMPLETE, as they are for ATLengArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlealternating-time temporal logicsbackward modalitiesstrategic reasoninggame logicshttp://dx.doi.org/10.1093/logcom/exu052