The combination of logic and optimization can provide significant contributions to rule-based Artificial Intelligence (AI). Logic serves as an obvious medium for encoding a rule base and drawing inferences, while optimization offers a powerful technology for computing these inferences. This synergy has gained new relevance amid growing concerns for transparency in AI, which is crucial for reproducibility, explainability, trustworthiness, and fairness.
Rule-based AI presents a natural solution to transparency, becoming increasingly viable due to today's advanced optimization methods. This article surveys several areas of the logic-optimization partnership, including probabilistic logic, Bayesian logic, belief logics, Dempster-Shafer theory, nonmonotonic (default) logic, many-valued logics, and the inference of logical formulas from noisy data via Boolean regression.
It illustrates how to compute projections, the fundamental problem in both logic and optimization, using decision diagrams and logic-based Benders decomposition. The paper also describes the use of postoptimality analysis to explain how conclusions are reached, enhancing transparency further, as well as the role of optimization in answer set programming modulo theories. Finally, it suggests possible future research directions.
Blogger's Review: The integration of logic and optimization offers a clear path towards transparency in AI. By combining rigorous theoretical foundations with modern computational techniques, the exploration of fair and trustworthy AI is being advanced. In-depth research in this area not only enhances the explainability of AI but also lays a solid groundwork for future applications.