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

TL;DR

This paper explores two mathematical semantics for epistemic ensembles of knowledge-based agents, establishing their equivalence and demonstrating how they simulate each other and satisfy the same dynamic epistemic formulas.

Contribution

It introduces a formal framework relating semantic and symbolic environments of epistemic ensembles using { extPhi}-equivalence, with proofs of their simulation capabilities.

Findings

{ extPhi}-equivalent configurations simulate each other.

They satisfy the same dynamic epistemic ensemble formulas.

The paper provides formal proofs of these equivalences.

Abstract

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.