An epistemic ensemble is composed of knowledge-based agents capable of retrieving and sharing knowledge and beliefs about themselves and their peers. These agents access a global knowledge state and use actions to communicate and cooperate, altering the collective knowledge state. We study two types of mathematical semantics for epistemic ensembles based on a common syntactic operational ensemble semantics: a semantic environment defined by a class of global epistemic states, and a symbolic environment consisting of a set of epistemic formulæ. For relating these environments, we use the concept of \(\varPhi \) -equivalence, where a class of epistemic states and a knowledge base are \(\varPhi \) -equivalent, if any formula of \(\varPhi \) holds in the class of epistemic states if, and only if, it is an element of the knowledge base. Our main theorem shows that \(\varPhi \) -equivalent configurations simulate each other and satisfy the same dynamic epistemic ensemble formulae.