Which is the least complex explanation? Abduction and complexity

Abstract

It may happen that for a certain abductive problem there are several possible explanations, not all of them mutually compatible. What explanation is selected and which criteria are used to select it? This is the well-known problem of the selection of abductive hypotheses. Are there criteria that can help us to select the simplest explanation in a broad spectrum of abductive problems? To give an (affirmative) answer to this question we will move to a field in theoretical computer science: Algorithmic Information Theory (AIT). The algorithmic complexity measure K(s) can be used to determine which is the best theory within those explaining a set of observations. We introduce an application of K(s) to the selection of the best abductive explanation, in the context of dynamic epistemic logic (DEL).