Abductive Reasoning in Dynamic Epistemic Logic

This chapter proposes a study of abductive reasoning addressing it as an epistemic process that involves both an agent’s information and the actions that modify this information. More precisely, this proposal presents and discusses definitions of an abductive problem and an abductive solution in terms of an agent’s information (her knowledge and beliefs) and the involved epistemic actions (observation and belief revision). The discussion is then formalized with tools from dynamic epistemic logic; under such framework, the properties of the given definitions are studied, an epistemic action representing the application of an abductive step is introduced, and an illustrative example is provided. A number of the most interesting properties of abductive reasoning (those highlighted by Peirce) are shown to be better modeled within this approach.