Big Brother Logic: Logical modeling and reasoning about agents equipped with surveillance cameras in the plane

Abstract

We consider multi-agent scenarios where each agent controls a surveillance camera positioned in the plane, with fixed po-sition and angle of view, but rotating freely. The agents can thus observe the surroundings and each other. They can also reason about each other’s observation abilities and knowledge derived from these observations. We introduce suitable logical languages for reasoning about such scenarios which involve atomic formulae stating what agents can see, multi-agent epistemic operators for individual, distributed and common knowledge, as well as dynamic operators re-flecting the ability of cameras to turn around in order to reach positions satisfying formulae in the language. We in-troduce 3 different but equivalent versions of the semantics for these languages, discuss their expressiveness and provide translations in PDL style. Using these translations we de-velop algorithms and obtain complexity results for model checking and satisfiability testing for the basic logic BBL that we introduce here and for some of its extensions. No-tably, we show that even for the extension with common knowledge, model checking remains in PSPACE. Finally, we discuss some further extensions: by adding obstacles, posi-tioning the cameras in 3D or enabling them to change po-sitions. Our work has potential applications to automated reasoning, formal specification and verification of observa-tional abilities and knowledge of multi-robot systems.