Knowing the Model

TL;DR

This paper proposes a general framework for epistemic models that extends beyond traditional Kripke models, emphasizing the importance of the 'fully explanatory property' and enabling better representation of partial, asymmetric, and aware knowledge states.

Contribution

It introduces a broader class of epistemic models based on sets of possible worlds, highlighting the role of the fully explanatory property and expanding the modeling of knowledge.

Findings

Not all epistemic situations are Kripke models.

The fully explanatory property characterizes when a set of worlds forms a Kripke model.

New models can represent partial, asymmetric, and aware knowledge.

Abstract

Epistemic modal logic normally views an epistemic situation as a Kripke model. We consider a more basic approach: to view an epistemic situation as a set W of possible states/worlds -- maximal consistent sets of propositions -- with conventional accessibility relations determined by W. We find that in many epistemic situations, W is not a Kripke model: a necessary and sufficient condition for W to be a Kripke model is the so-called `fully explanatory property' - a propositional form of common knowledge of the model - which has been a hidden (and overlooked) assumption in epistemic modal logic. We sketch a theory that describes epistemic models in their generality. We argue for conceptual and practical value of new models, specifically for representing partial knowledge, asymmetric knowledge, and awareness.