Interpretations of epistemic mu-calculus over multi-agent games

Abstract: In this work, we are interested in expressing and studying certain formal properties of multi-agent games. In particular, we are interested in the case in which a team of agents with imperfect information is playing against the environment. This is modeled by a non-deterministic game, where the agents can only partially distinguish its states, to varying degrees. We will study these games under the lens of the multi-agent knowledge-based subset construction (MKBSC), which, when applied to a game, reduces the degree of imperfect information the agents have. An appropriate language to express interesting and complex properties in these type of games is the epistemic μ-calculus, an extension of classicepistemic logic with a recursive operator. We define two semantics forthis language, one corresponding to a global view of the game, and onecorresponding to a local one. We state a claim relating these two semantics,while proving an analogous statement for epistemic logic.