Some Remarks on the Model Theory of Epistemic Plausibility Models

TL;DR

This paper systematically explores the model theory of epistemic plausibility models, focusing on bisimulation, and highlights challenges and solutions related to conditional belief and dynamic changes.

Contribution

It introduces various bisimulation notions for epistemic plausibility models, proves key theoretical results, and addresses the limitations of bisimulation when conditional belief is involved.

Findings

Bisimulation implies logical equivalence in epistemic plausibility models.

Hennessy-Milner type theorem established for these models.

Bisimulation cannot be directly generalized with conditional belief without modifications.

Abstract

Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic plausibility models have been introduced. Because these 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. We define various notions of bisimulations (parametrized by a language L) and show that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type result, and also two undefinability results. However, our main point is a negative one, viz. that bisimulations cannot straightforwardly be generalized to epistemic plausibility models if conditional belief is taken into account. We present two ways of coping with this issue: (i) adding a modality to the language, and (ii) putting extra constraints on the models. Finally, we make some remarks about the interaction between bisimulation and dynamic model changes.