We formalize the notion of a Cartesian situation in the situation calculus, a property that imposes strong structural conditions on the configuration of a set of possible worlds. Focusing on action theories that use the Scherl and Levesque account of knowledge and action, we show how Cartesian situations give rise to a set of decomposition properties for simplifying epistemic formulae (in particular, certain disjunctive and existentially quantified formulae) into equivalent components that only mention fluent literals. Moreover, we describe certain expressive classes of action theories that preserve the Cartesian property through action. This work also offers the possibility of identifying action theories that can be compiled into alternative accounts of knowledge that have similar representational restrictions, but do not use possible worlds.
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