Agents that look at one another

Despite the fact that epistemic connectives are sometimes interpreted in concrete structures defined by means of runs and clock time functions, one of the things that strikes one when studying multiagent logics is how abstract their semantics are. Contrasting this fact is the fact that real agents like robots in everyday life and virtual characters in video games have strong links with their spatial environment. In this article, we introduce multiagent logics which semantics can be defined by means of purely geometrical notions: possible states are defined by means of the positions in ℝn occupied by agents and the sections of ℝn seen by agents whereas accessibility relations are defined by means of the ability of agents to imagine possible states compatible with what they currently see.