Symbolic control is an approach to the control of continuous or hybrid systems with specifications expressed in a logic form. This approach is based on the use of symbolic models describing the dynamical system behavior with a finite description of the transition relation between its states. In the literature, many results using this approach assume the availability of full and exact information about the system states to compute the control actions. In this paper, we consider a more realistic scenario where only partial information about the plant states is available. This paper proposes an abstraction that makes it possible to synthesize output-feedback controllers. The presence of disturbances and output noise is also considered. A direct path between observer designs in the classical theory and control synthesis in formal methods is established and a numerical example is provided to illustrate the results.