A Modal Logic for Subject-Oriented Spatial Reasoning

We present a modal logic for representing and reasoning about space seen from the subject’s perspective. The language of our logic comprises modal operators for the relations “in front”, “behind”, “to the left”, and “to the right” of the subject, which introduce the intrinsic frame of reference; and operators for “behind an object”, “between the subject and an object”, “to the left of an object”, and “to the right of an object”, employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete. 2012 ACM Subject Classification Theory of computation → Complexity theory and logic; Theory of computation → Modal and temporal logics; Theory of computation → Automata over infinite objects; Theory of computation → Verification by model checking