用逻辑与优化结合提升AI可解释性，让决策过程透明可信。
Logic, Optimization, and Artificial Intelligence
- 将逻辑规则与优化技术融合，实现可解释推理
- 通过决策图和分解法高效求解逻辑投影问题
- 适合关注AI透明性与可信决策的研究者
逻辑与优化的结合可为基于规则的AI带来重要贡献。逻辑是编码规则库并从中推断的核心工具，而优化则提供了强大的推理计算能力。二者结合在当前对AI透明性的日益关注背景下显得尤为关键，透明性关乎可复现性、可解释性、可信度与公平性。基于规则的AI天然具备透明性优势，如今得益于先进的优化方法，其实用性显著提升。本文综述了逻辑-优化合作的多个领域，包括概率逻辑、贝叶斯逻辑、信念逻辑、Dempster-Shafer理论、非单调（默认）逻辑、多值逻辑，以及基于布尔回归从噪声数据中推导逻辑公式的算法。文章展示了如何利用决策图和基于逻辑的Benders分解求解基本的投影问题；描述了事后分析在解释结论形成过程中的作用，进一步增强透明性；还探讨了优化在答案集编程模理论中的角色。最后提出若干未来研究方向。
原文摘要 · Abstract (English)
Logic and optimization can, in combination, make valuable contributions to rule-based AI. Logic is the obvious medium for encoding a rule base and drawing inferences from it, while optimization provides a powerful technology for computing inferences. Their combination has taken on new relevance amid a growing concern for transparency in AI. which is important for reproducibility, explainability, trustworthiness, and fairness. Rule-based AI provides a natural solution to transparency that is becoming increasingly practical due to today's highly advanced optimization methods. This article surveys several areas of logic-optimization partnership, including probabilistic logic, Bayesian logic, belief logics and Dempster-Shafer theory, nonmonotonic (default) logic, many-valued logics, and inference of logical formulas from noisy data based on Boolean regression. It shows how to compute projections, the fundamental problem of both logic and optimization, using decision diagrams and logic-based Benders decomposition. It describes the use of postoptimality analysis to explain how conclusions are reached, further enhancing transparency, as well as the role of optimization in answer set programming modulo theories. The paper concludes by suggesting possible future research directions.
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