Epistemic Learning Programs A Calculus for Describing Epistemic Action Models

TL;DR

This paper introduces learning programs as a new formalism to describe epistemic actions in multi-agent systems, extending dynamic epistemic logic to encompass complex learning scenarios.

Contribution

It proposes the concept of learning programs and demonstrates that all finite K45 action models can be represented using them.

Findings

All finite K45 action models can be described by learning programs.

Learning programs can model various types of information change, including private, concurrent, and incorrect learning.

The framework extends existing models of epistemic action to more complex learning scenarios.

Abstract

Dynamic Epistemic Logic makes it possible to model and reason about information change in multi-agent systems. Information change is mathematically modeled through epistemic action Kripke models introduced by Baltag et al. Also, van Ditmarsch interprets the information change as a relation between epistemic states and sets of epistemic states and to describe it formally, he considers a special constructor LB called learning operator. Inspired by this, it seems natural to us that the basic source of information change in a multi-agent system should be learning an announcement by some agents together, privately, concurrently or even wrongly. Hence moving along this path, we introduce the notion of a learning program and prove that all finite K45 action models can be described by our learning programs