Defined by Gelfond in 1991 (G91), epistemic specifications (or programs) are an extension of logic programming under stable models semantics that introduces subjective literals. A subjective literal allows checking whether some regular literal is true in all (or in some of) the stable models of the program, being those models collected in a set called world view. One epistemic program may yield several world views but, under the original G91 semantics, some of them resulted from self-supported derivations. During the last eight years, several alternative approaches have been proposed to get rid of these self-supported world views. Unfortunately, their success could only be measured by studying their behaviour on a set of common examples in the literature, since no formal property of “self-supportedness” had been defined. To fill this gap, we extend in this paper the idea of unfounded set from standard logic programming to the epistemic case. We define when a world view is founded with respect to some program and propose the foundedness property for any semantics whose world views are always founded. Using counterexamples, we explain that the previous approaches violate foundedness, and proceed to propose a new semantics based on a combination of Moore’s Autoepistemic Logic and Pearce’s Equilibrium Logic. The main result proves that this new semantics precisely captures the set of founded G91 world views.