A possible worlds semantics for model-based spatial reasoning is presented. In this semantics, worlds are characterized by the alternative states that result from indeterminacy or partial knowledge. A world is represented as a set of symbolic arrays, where symbols in the array map to entities in the world and the relative locations of symbols correspond to the relative locations of entities. Deduction is carried out using a model-theoretic approach in which array representations are "inspected" using primitive array functions. Nonmonotonic reasoning using array representations is also discussed.