Epistemic Ensembles in Semantic and Symbolic Environments (Extended Version with Proofs)

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 Φ-equivalence, where a class of epistemic states and a knowledge base are Φ-equivalent, if any formula of Φ holds in the class of epistemic states if, and only if, it is an element of the knowledge base. Our main theorem shows that Φ-equivalent configurations simulate each other and satisfy the same dynamic epistemic ensemble formulae.