Big Brother Logic: Logical modeling and reasoning about agents equipped with surveillance cameras in the plane Technical report IRIT/RT-2014-01-FR
Olivier Gasquet, Valentin Goranko, Schwarzentruber Ens Rennes · 2014
We consider multi-agent scenarios where each agent controls a surveillance camera positioned in the plane, with xed position 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 reecting the ability of cameras to turn around in order to reach positions satisfying formulae in the language. We introduce 3 dierent but equivalent versions of the semantics for these languages, discuss their expressiveness and provide translations in PDL style. Using these translations we develop algorithms and obtain complexity results for model checking and satisability testing for the basic logic BBL that we introduce here and for some of its extensions. Notably, we show that even for the extension with common knowledge, model checking remains in PSPACE. Finally, we discuss some further extensions: by adding obstacles, positioning the cameras in 3D or enabling them to change positions. Our work has potential applications to automated reasoning, formal specication and verication of observational abilities and knowledge of multi-robot systems.