Epistemic Actions: Comparing Multi-agent Belief Bases with Action Models

We compare the syntactic multi-agent belief base approach, and the dynamic epistemic logic possible world semantic approach. In the belief base approach, the language provides an implicit and an explicit belief operators, plus a dynamic modality for actions consisting in adding formulae to bases. For the semantic approach, we rely on 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 addition of a formula in a belief base. Conversely, we identify a fragment of DEL that can be translated in the multi- agent belief base language.