Graded Distributed Belief

The idea of using belief bases as formal semantics for multi-agent epistemic logic was first introduced in [26] and further developed in [27, 28]. This approach aligns with the sentential (or syntactic) perspective on knowledge representation [21, 13, 33, 20], which holds th at an agent's body of knowledge should be represented as a set of sentences in a formal language. The key novelty of belief base semantics, compared to traditional epistemic logic semantics based on multi-relational Kripke models [31, 12], lies in two main aspects. First, a possible world (or state) in a mo del is not treated as a primitive entity but is instead composed of the agents' belief bases and a valu ation of propositional atoms. Second, the agents' accessibility relations are not explicitly par t of the model but are determined a posteriori from their belief bases.