Abstract

This paper argues that the standard interpretation of modal logic S5 relies on an implicit assumption of global accessibility of possible worlds, which is incompatible with systems characterized by constraints, dynamics, and causal structure. We introduce a reachability-based semantics in which possibility is defined not by the existence of a consistent world, but by the existence of an admissible trajectory in a constrained state space. Within this framework, key S5 principles—most notably ◇□P → □P—fail to hold. We show that S5 collapses local necessity into global necessity and thereby excludes common structures of real systems, such as multi-stability and path-dependence. The result is not that S5 is formally incorrect, but that its applicability is limited to a highly idealized “configuration space” interpretation of modality.