  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 formul{\ae}. For relating these environments, we use the concept of
{\Phi}-equivalence, where a class of epistemic states and a knowledge base are
{\Phi}-equivalent, if any formula of {\Phi} holds in the class of epistemic
states if, and only if, it is an element of the knowledge base. Our main
theorem shows that {\Phi}-equivalent configurations simulate each other and
satisfy the same dynamic epistemic ensemble formulae.
