Approximating Perfect Recall when Model Checking Strategic Abilities: Theory and Applications

Abstract

The model checking problem for multi-agent systems against specifications in the alternating-time temporal logic AT L, hence AT L∗ , under perfect recall and imperfect information is known to be undecidable. To tackle this problem, in this paper we investigate a notion of bounded recall under incomplete information. We present a novel three-valued semantics for AT L∗ in this setting and analyse the corresponding model checking problem. We show that the three-valued semantics here introduced is an approximation of the classic two-valued semantics, then give a sound, albeit partial, algorithm for model checking two-valued perfect recall via its approximation as three-valued bounded recall. Finally, we extend MCMAS, an open-source model checker for AT L and other agent specifications, to incorporate bounded recall; we illustrate its use and present experimental results.

Towards the Combination of Model Checking and Runtime Verification on Multi-Agent Systems

“…Model Checking on MAS. Existing approaches to approximate AT L model checking under imperfect information and perfect recall have either focused on an approximation to perfect information [4,5] or developed notions of bounded recall [6]. Differently from these works, we do not restrain the class of problems tackled by our technique.…”

“…So, our procedure approximates the truth value by considering the case in which all the agents in the game collaborate to achieve the objectives not satisfied in the model checking phase. That is, while in [4,5] the approximation is given in terms of information, in [6] is given in terms of recall of the strategies, and in [17] the approximation is given by generalizing the logic, here we give results by approximating the coalitions. Furthermore, we recall that our procedure produces always results, even partial.…”

Reasoning about Human-Friendly Strategies in Repeated Keyword Auctions

“…We also consider SL instead of ATL, due to its expressive power. In a related vein, Ågotnes and Walther [2] investigate strategic abilities of agents with bounded memory, while Belardinelli et al [14] consider bounded memory as an approximation of perfect recall. On a related direction, temporal and strategic logics have been extended to handle agents with bounded resources [5,6,19,20].…”

Towards the Verification of Strategic Properties in Multi-Agent Systems with Imperfect Information

“…Given the relevance of the imperfect information setting, even partial solutions to the problem can be useful. Previous approaches have either focused on an approximation to perfect information [3,4] or to bounded recall [5]. In this contribution the main idea is to modify the topological structure of the models and use CTL verification.…”

“…Instead, we consider the whole class of iCGS and define a general verification procedure. In this sense, our approach is related to [5] where an incomplete bounded recall method is defined and to [3,4] where an approximation to perfect information is presented. However, while in these works perfect recall or imperfect information are approximated, here we study the topological structure of the iCGS and use CTL * verification to provide a verification result.…”