A Logic of Weighted Reasons for Explainable Inference in AI

We propose two methods that integrate justification logic, defeasible reasoning and numerical reasoning to lay the foundations for an explainable, reason-based neuro-symbolic architecture. The core idea behind the two methods is to model two different ways in which weighing default reasons can be formalized in justification logic. The two methods both assign weights to justification terms, i.e. modal-like terms that represent reasons for propositions. The first method obtains the values of these reasons solely on the basis of the extension-based operational semantics for default justification logic. This semantics handles default reasons in such a way that it extends consistent sets of reason-formula pairs as much as possible. The second method aims for a direct comparison of reasons, where the potential conflicts between default reasons are resolved by pooling together all the applicable reasons for or against propositions. Instead of applying default steps selectively in the fashion of the operational semantics, all available default reasons are applied simultaneously and interact directly with each other. We argue that the two methods show why combining justification logic, defeasible reasoning and numerical reasoning is an intuitive and promising logical approach to explainable neuro-symbolic integration.