Propositional Defeasible Explanation

Knowledge Representation and Reasoning is a field within AI in which information and reasoning is modeled using formal logic. In classical logics, we can use entailment to infer new information from our modeled information. Explanations provide a way of showing why an entailment holds and are a crucial aspect of reasoning systems. However, they have not yet been explored in detail for forms of defeasible reasoning such as KLM. We evaluate prior work on the topic with a focus on KLM propositional logic, utilizing three definitions for defeasible entailment within the KLM framework called Rational Closure, Lexicographic Closure and Relevant Closure, and find that a form of defeasible explanation initially described for Rational Closure which we term weak justification can be adapted to Relevant and Lexicographic Closure. We then show that weak justification obeys a number of intuitive properties derived from the KLM postulates and also consider how a more general definition of defeasible explanation known as strong explanation applies to KLM and propose an algorithm that enumerates these justifications for Rational Closure. Another of our results proposes a general definition of defeasible explanation distinct from strong and weak justification. These contributions enhance our understanding of explanation for KLM and may also serve as the basis for the practical implementations of explanation services for reasoning systems.