  Explanation generation frameworks aim to make AI systems' decisions
transparent and understandable to human users. However, generating explanations
in uncertain environments characterized by incomplete information and
probabilistic models remains a significant challenge. In this paper, we propose
a novel framework for generating probabilistic monolithic explanations and
model reconciling explanations. Monolithic explanations provide self-contained
reasons for an explanandum without considering the agent receiving the
explanation, while model reconciling explanations account for the knowledge of
the agent receiving the explanation. For monolithic explanations, our approach
integrates uncertainty by utilizing probabilistic logic to increase the
probability of the explanandum. For model reconciling explanations, we propose
a framework that extends the logic-based variant of the model reconciliation
problem to account for probabilistic human models, where the goal is to find
explanations that increase the probability of the explanandum while minimizing
conflicts between the explanation and the probabilistic human model. We
introduce explanatory gain and explanatory power as quantitative metrics to
assess the quality of these explanations. Further, we present algorithms that
exploit the duality between minimal correction sets and minimal unsatisfiable
sets to efficiently compute both types of explanations in probabilistic
contexts. Extensive experimental evaluations on various benchmarks demonstrate
the effectiveness and scalability of our approach in generating explanations
under uncertainty.
