"Concerning the first objective, we defined an extension of Strategy Logic for imperfect information, called SLii, in which one can say what observation power a strategy should have. For this very expressive logic, it is undecidable to check whether a given system satisfies a given formula (a problem called model checking). But by taking inspiration from the theory of games with imperfect information and distributed synthesis we defined a fragment of SLii for which we proved the model checking to be decidable.
The main results obtained concerning this objective have been published in the following article, presented at the international conference LICS 2017:
Raphaël Berthon, Bastien Maubert, Aniello Murano, Sasha Rubin and Moshe Vardi, “Strategy Logic with Imperfect Information”, LICS 2017
In addition, the methods developed to study SLii have allowed us to derive similar results for other logics of strategic reasoning. These results have been presented at the international conference AAMAS 2017:
Raphaël Berthon, Bastien Maubert and Aniello Murano, ""Decidability results for ATL* with imperfect information and perfect recall"", AAMAS 2017.
An extended version of this work with applications of the main result to the resolution of several strategic problems such as existence of Nash equilibria and rational synthesis, is about to be submitted to the international journal ACM Transactions on Computational Logic.
Concerning the second objective of the project, we first had to study a new phenomenon in temporal epistemic logics. In SLii, agents' observations can change along time when agents change strategy. Such dynamic changes of observation power had never been studied in logics of knowledge and time, and we thus had to start by understanding what they mean for the semantics of knowledge. As a first step we thus left aside the strategic aspect and studied this phenomenon in the simpler setting of epistemic temporal logic. We introduced a new operator that indicates an agent changing observation power, we defined a natural semantics for this logic, we showed that this observation-change operator increases the expressivity of the logic, and we solved the model-checking problem.
The next step has been to integrate epistemic operators with observation change in our logic SLii. We studied an epistemic extension of SLii, and we solved its model-checking problem, once more for a fragment based on the concept of hierarchical information. This work is the object of two submissions to the international conference KR 2018.
In addition we also made progress in a direction that was not foreseen in the initial project’s objectives, even though it still is about extending Strategy Logic to make it more fit to study realistic problems of multi-agent systems.
One limitation of Strategy Logic is that it is purely qualitative. We extended Strategy Logic to include quantitative aspects in a way that can express bounds on “how quickly” and “how many”. We devised a general technique, based on the study of automata with counters, that solves the model-checking problems for this logic. This work will be presented at the international conference CSL 2018.
Nathanaël Fijalkow, Bastien Maubert, Aniello Murano and Sasha Rubin, “Quantifying Bounds in Strategy Logic”, CSL 2018.
In addition, all these results will be presented at the international workshop Strategic Reasoning 2018, which will take place in Oxford in July as part of the Federated Logic Conference 2018 (FLOC).
"
