Towards a Logic for Reasoning About Learning in a Changing World

14 pages•Published: May 15, 2012

Abstract

We develop an algebraic modal logic that combines epistemic and dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that ``change the state'' of the underlying system and not just the state of knowledge of the agents. The key novel feature that emerges is the need to have a way of ``inverting transitions'' and distinguishing between transitions that ``really happen'' and transitions that are possible.

Our approach is algebraic, rather than being based on a Kripke-style semantics. The semantics are given in terms of quantales. We introduce a class of quantales with the appropriate inverse operations and use it to model toy robot-navigation problems, which illustrate how an agent learns information by taking actions. We discuss how a sound and complete logic of the algebra may be obtained from the positive fragment of PDL with converse.

Keyphrases: Algebraic Modal Logic, dynamic epistemic logic, Information Learning, Quantale-Module, robot navigation

In: Berndt Müller (editor). LAM'10. 3rd International Workshop on Logics, Agents, and Mobility, vol 7, pages 82--95

Links:	https://easychair.org/publications/paper/sx6F
	https://doi.org/10.29007/8g5j