Some remarks on the model theory of epistemic plausibility models

Traditional epistemic logic can be seen as a particular branch of modal logic. Its semantics is defined in terms of Kripke models, and philosophical principles about knowledge (e.g. factivity: Kφ→ φ) are shown to correspond to properties of the epistemic accessibility relation (e.g. reflexivity). By adding another (doxastic) accessibility relation, also belief can be treated in this framework. Belief is not assumed to be factive, but at least consistent (¬B⊥), which corresponds to requiring the doxastic accessibility relation to be serial instead of reflexive. In this extended framework, one can study the interaction between knowledge and belief (e.g. is Kφ → Bφ a valid principle?); cf. [5, 8]. Furthermore, since this framework is still ‘just’ a (multi-)modal logic, it inherits the mathematically well-developed model theory of modal logic. However, it is well-known that dynamic phenomena cannot be captured in this framework; cf. section 3.1 of [7]. To remedy this, epistemic plausibility models have been introduced (technical details will be presented later). In these models, one can again study knowledge, belief (and even other cognitive propositional attitudes), and their various interactions. Furthermore, this framework provides a realistic model of various dynamic phenomena, and thus solves the main problem of the previous approach. However, because epistemic plausibility models are much richer structures than Kripke models, they do not straightforwardly inherit the model-theoretical results of modal logic. Therefore, while epistemic plausibility structures are well-suited for modeling purposes, an extensive investigation of their model theory has been lacking so far. The aim of the present paper is to fill exactly this gap, by initiating a systematic exploration of the model theory of epistemic plausibility models. Like in ‘ordinary’ modal logic, the focus will be on the notion of bisimulation — it turns out that finding the right generalization of this notion is not a trivial task. In Section 2, we introduce epistemic plausibility models and discuss some important operators which can be interpreted on such models, and their