🤖 AI Summary
This work addresses the limitations of conventional artificial intelligence systems—particularly their lack of logical rigor and traceability—by proposing a novel framework that integrates logical reasoning with optimization computation to build transparent, interpretable, trustworthy, and fair rule-based AI. The approach leverages decision diagrams and logic-based Benders decomposition for efficient projection computation and enhances explainability through post-optimality analysis. It unifies diverse formalisms including probabilistic logic, non-monotonic logic, multi-valued logic, Bayesian logic, Dempster–Shafer theory, and answer set programming modulo theories to automatically infer logical rules from noisy data. The resulting system not only supports efficient and transparent rule-based reasoning but also provides formal, traceable justifications for every conclusion, substantially improving the practicality and trustworthiness of AI.
📝 Abstract
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.