We compare the syntactic approach to the representation of epistemic states in the multi-agent domain with the possible-world semantic approach. The syntactic approach exploits belief bases and models belief change by means of dynamic operators for belief base expansion. The semantic approach relies on multi-relational Kripke models and represents belief change through so-called action models of Dynamic Epistemic Logic (DEL). We first show how to translate a formula of the belief base approach into DEL: in particular, we provide a specific action model scheme corresponding to the process of expanding an agent's belief base with a formula. Conversely, we identify a fragment of DEL that can be translated into the multi-agent dynamic epistemic language interpreted on belief bases.