Thesis
Thesis Title: An Algebraic Approach to Dynamic Epistemic Logic
Supervised by:Prof. Prakash Panangaden and Prof. Doina Precup
Past approaches to dynamic epistemic logic have typically been focused on actions whose primary purpose is to communicate information from one agent to another. These actions are unable to alter the valuation of any proposition within the system. In fields such as security and economics, it is easy to imagine situations in which this sort of action would be insufficient. Instead, we expand the framework to include both communication actions and actions that change the state of the system. Furthermore, we propose a new modality which captures both epistemic and propositional changes that result from the agentsŐ actions.
The entire thesis is available here.
Abstract:
In reasoning about multi-agent systems, it is important to look beyond the realm of propositional logic and to reason about the knowledge of agents within the system, as what they know about the environment will affect how they behave. A useful tool for formalizing and analyzing what agents know is epistemic logic, a modal logic developed by philosophers in the early 1960s. Epistemic logic is key to understanding knowledge in multi-agent systems, but insufficient if one wishes to study how the agentsŐ knowledge changes over time. To do this, it is necessary to use a logic that combines dynamic and epistemic modalities, called dynamic epistemic logic. Some formalizations of dynamic epistemic logic use Kripke semantics for the states and actions, while others take a more algebraic approach, and use order-theoretic structures in their semantics. We discuss several of these logics, but focus predominantly on the algebraic framework for dynamic epistemic logic.Past approaches to dynamic epistemic logic have typically been focused on actions whose primary purpose is to communicate information from one agent to another. These actions are unable to alter the valuation of any proposition within the system. In fields such as security and economics, it is easy to imagine situations in which this sort of action would be insufficient. Instead, we expand the framework to include both communication actions and actions that change the state of the system. Furthermore, we propose a new modality which captures both epistemic and propositional changes that result from the agentsŐ actions.
The entire thesis is available here.