Reasoning about memoryless strategies under partial observability and unconditional fairness constraints

Abstract

Alternating-time Temporal Logic is a logic to reason about strategies that agents can adopt to achieve a specified collective goal. A number of extensions for this logic exist; some of them combine strategies and partial observability, some others include fairness constraints, but to the best of our knowledge no work provides a unified framework for strategies, partial observability and fairness constraints. Integration of these three concepts is important when reasoning about the capabilities of agents without full knowledge of a system, for instance when the agents can assume that the environment behaves in a fair way. We present ATLK irF , a logic combining strategies under partial observability in a system with fairness constraints on states. We introduce a model-checking algorithm for ATLK irF by extending the algorithm for a full-observability variant of the logic and we investigate its complexity. We validate our proposal with an experimental evaluation.

Approximate verification of strategic abilities under imperfect information

“…Some early attempts at verification of imperfect information strategies made their way into the MCMAS model-checker [25,28,23,24], but the issue was never at the heart of the tool. More dedicated attempts began to emerge only recently [26,8,17,9]. Up until now, experimental results confirm that the initial intuition was right: model checking of strategic modalities for imperfect information is hard, and dealing with it requires innovative algorithms and verification techniques.…”

Comparing approaches for model-checking strategies under imperfect information and fairness constraints

“…While these logics have been studied for 15 years, practi-cal approaches to solve their model-checking problem only appeared recently. This paper briefly described the three approaches of Pilecki et al [27], Huang and van der Meyden [20,19], and Busard et al [8], adapted to AT LK irF , an extension of AT L with memoryless uniform strategies and unconditional fairness constraints on states [9]. It also presented their implementation with PyNuSMV, a Python library for prototyping BDD-based model-checking algorithms based on NuSMV [6].…”

“…AT LK irF semantics follows the ideas of AT L, where two strategic sub-formulas can be satisfied because of two different strategies, while the semantics of Lomuscio and Raimondi diverges from it. Furthermore, their idea is similar to the first idea proposed by Busard et al [7,9], shown to be highly ineffective compared to the partial approach [8].…”

Natural strategic ability

“…Imperfect information strategies have been also studied within the SL framework [18,21]. Moreover, many conceptual extensions have been considered, e.g., with explicit reasoning about strategies [117,127], rationality assumptions and solution concepts [122,41], coalition formation and negotiation [34], opponent modeling and action in stochastic environments [73,38,112,111], fairness conditions and prompt temporal operators [42,13], reasoning about irrevocable plans and interplay between strategies of different agents [2,33], and agents with bounded resources (for the latter, see the references mentioned below). Strategic abilities of resource-bounded agents.…”