Epistemic Skills: Logical Dynamics of Knowing and Forgetting

TL;DR

A type of epistemic logics that encapsulates both the dynamics of acquiring knowledge and losing information (knowing) and losing information (forgetting), alongside the integration of group knowledge concepts is presented.

Abstract

We present a type of epistemic logics that encapsulates both the dynamics of acquiring knowledge (knowing) and losing information (forgetting), alongside the integration of group knowledge concepts. Our approach is underpinned by a system of weighted models, which introduces an "epistemic skills" metric to effectively represent the epistemic abilities associated with knowledge update. In this framework, the acquisition of knowledge is modeled as a result of upskilling, whereas forgetting is by downskilling. Additionally, our framework allows us to explore the concept of "knowability," which can be defined as the potential to acquire knowledge through upskilling, and facilitates a nuanced understanding of the distinctions between epistemic de re and de dicto expressions. We study the computational complexity of model checking problems for these logics, providing insights into both the theoretical underpinnings and practical implications of our approach.

Figures (1)

• Figure 1: Illustration of the model $M$.

Theorems & Definitions (21)

• Definition 1
• Definition 2
• Proposition 3
• Remark 1
• Lemma 4
• Definition 5
• Proposition 6
• Lemma 7
• proof
• Lemma 8