Observable Models

Epistemic reading of Kripke models relies on a hidden assumption of common knowledge of the model which is too restrictive in epistemic contexts since agents may have different views of the situation. We explore possible worlds models in their full generality without common knowledge assumptions. Our starting point is a collection of possible worlds with accessibility relations "whatever is known in u is true in v." We call such a structure an observable model since, contrary to the popular belief, it is not generally a Kripke model but rather an "observable section" of some Kripke model. We sketch a theory of observable models and argue that they bring a new conceptual clarity to epistemic modeling. In practical terms, observable models are as manageable as Kripke models and have advantages over the latter in representing (un)awareness and ignorance. Similar analysis applies to intuitionistic models.