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We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, this problem is undecidable; but we introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model, and we prove that model-checking SLii restricted to hierarchical instances is decidable. To establish this result we go through QCTL, an intermediary, "low-level" logic much more adapted to automata techniques. QCTL is an extension of CTL with second-order quantification over atomic propositions. We extend it to the imperfect information setting by parameterising second-order quantifiers with observations. While the model-checking problem of QCTLii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. We apply our result to solve complex strategic problems in the imperfect-information setting. We first show that the existence of Nash equilibria for deterministic strategies is decidable in games with hierarchical information. We also introduce distributed rational synthesis, a generalisation of rational synthesis to the imperfect-information setting. Because it can easily be expressed in our logic, our main result provides solution to this problem in the case of hierarchical information.

We study dynamic changes of agents’ observational power in logics of knowledge and time. We consider CTLK*, the extension of CTL* with knowledge operators, and enrich it with a new operator that models a change in an agent’s way of observing the system. We extend the classic semantics of knowledge for agents with perfect recall to account for changes of observational power, and we show that this new operator increases the expressivity of CTLK*. We reduce the model-checking problem for our logic to that for CTLK*, which is known to be decidable. This provides a solution to the model-checking problem for our logic, but it is not optimal, and we provide a direct model-checking procedure with better complexity.

Two distinct semantics have been considered for knowledge in the context of strategic reasoning, depending on whether players know each other's strategy or not. In the former case, that we call the informed semantics, distributed synthesis for epistemic temporal specifications is undecidable, already on systems with hierarchical information. However, for the other, uninformed semantics, the problem is decid-able on such systems. In this work we generalise this result by introducing an epistemic extension of Strategy Logic with imperfect information. The semantics of knowledge operators is uninformed, and captures agents that can change observation power when they change strategies. We solve the model-checking problem on a class of "hierarchical in-stances", which provides a solution to a vast class of strategic problems with epistemic temporal specifications, such as distributed or rational synthesis, on hierarchical systems.

Program synthesis constructs programs from specifications in an automated way. Strategy Logic (SL) is a powerful and versatile specification language whose goal is to give theoretical foundations for program synthesis in a multi-agent setting. One limitation of Strategy Logic is that it is purely qualitative. For instance it cannot specify quantitative properties of executions such as "every request is quickly granted", or quantitative properties of trees such as "most executions of the system terminate". In this work, we extend Strategy Logic to include quantitative aspects in a way that can express bounds on "how quickly" and "how many". We define Prompt Strategy Logic, which encompasses Prompt LTL (itself an extension of LTL with a prompt eventuality temporal operator), and we define Bounded-Outcome Strategy Logic which has a bounded quantifier on paths. We supply a general technique, based on the study of automata with counters, that solves the model-checking problems for both these logics.

Two distinct semantics have been considered for knowledge in the context of strategic reasoning, depending on whether players know each other's strategy or not. The problem of distributed synthesis for epistemic temporal specifications is known to be undecidable for the latter semantics, already on systems with hierarchical information. However, for the other, uninformed semantics, the problem is decidable on such systems. In this work we generalise this result by introducing an epistemic extension of Strategy Logic with imperfect information. The semantics of knowledge operators is uninformed, and captures agents that can change observation power when they change strategies. We solve the model-checking problem on a class of "hierarchical instances", which provides a solution to a vast class of strategic problems with epistemic temporal specifications on hierarchical systems, such as distributed synthesis or rational synthesis.

Alternating-time Temporal Logic (ATL*) is a central logic for multiagent systems. Its extension to the imperfect information setting (ATL*i ) is well known to have an undecidable model-checking problem when agents have perfect recall. Studies have thus mostly focused either on agents without memory, or on alternative semantics to retrieve decidability. In this work we establish new decidability results for agents with perfect recall: We first prove a meta-theorem that allows the transfer of decidability results for classes of multiplayer games with imperfect information, such as games with hierarchical observation, to the model-checking problem for ATL*i . We then establish that model checking ATL* with strategy context and imperfect information is decidable when restricted to hierarchical instances.

We study dynamic changes of agents' observational power in logics of knowledge and time. We consider CTL*K, the extension of CTL* with knowledge operators, and enrich it with a new operator that models a change in an agent's way of observing the system. We extend the classic semantics of knowledge for perfect-recall agents to account for changes of observation, and we show that this new operator strictly increases the expressivity of CTL*K. We reduce the model-checking problem for our logic to that for CTL*K, which is known to be decidable. This provides a solution to the model-checking problem for our logic, but its complexity is not optimal. Indeed we provide a direct decision procedure with better complexity.

Two distinct semantics have been considered for knowledge in the context of strategic reasoning, depending on whether players know each other’s strategy or not. The problem of distributed synthesis for epistemic temporal specifications is known to be undecidable for the latter semantics, already on systems with hierarchical information. However, for the other, uninformed semantics, the problem is decidable on such systems. In this work we generalise this result by introducing an epistemic extension of Strategy Logic with imperfect information. The semantics of knowledge operators is uninformed, and captures agents that can change observation power when they change strategies. We solve the model-checking problem on a class of "hierarchical instances", which provides a solution to a vast class of strategic problems with epistemic temporal specifications on hierarchical systems, such as distributed synthesis or rational synthesis.

We introduce an extension of Strategy logic for the imperfect-information setting, called SL ii , and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of " hierarchical instances " for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SL ii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL * ii , an extension of QCTL (itself an extension of CTL with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL * ii allows us to provide a conceptually neat reduction of SL ii to QCTL * ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL * ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SL ii follows since the reduction maps hierarchical instances of SL ii to hierarchical formulas of QCTL * ii .

Strategic reasoning is one of the most active research areas in multi-agent system domain. The literature in this field is extensive and provides a plethora of logics for modelling strategic ability. Theoretical results are now being used in many exciting domains, including software tools for information system security, robot teams with sophisticated adaptive strategies, and automatic players capable of beating expert human adversaries, just to cite a few. All these examples share the challenge of developing novel theories and tools for agent-based reasoning that take into account the likely behaviour of adversaries. The SR international workshop aims to bring together researchers working on different aspects of strategic reasoning in computer science, both from a theoretical and a practical point of view. Please visit https://sites.google.com/site/sr2016homepage/

Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend it to include imperfect information by parameterizing quantifiers with an observation that defines how well they observe the model, thus constraining their behaviour. We consider two different semantics, one related to the notion of no memory, the other to perfect recall. We study the expressiveness of our logic, and show that it coincides with MSO for the first semantics and with MSO with equal level for the second one. We establish that the model-checking problem is Pspace-complete for the first semantics. While it is undecidable for the second one, we identify a syntactic fragment, defined by a notion of hierarchical formula, which we prove to be decidable thanks to an automata-theoretic approach.