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This paper explores the intersection of logic-based reasoning and advanced optimization techniques to enhance rule-based AI systems, specifically addressing critical needs for transparency, explainability, and fairness. By leveraging methods such as decision diagrams and postoptimality analysis, it demonstrates how computational inference can be made more reproducible and trustworthy without sacrificing performance. The work is particularly relevant for researchers developing interpretable models where black-box neural networks are insufficient or undesirable.
Logic, Optimization, and Artificial Intelligence
arXiv:2607.15532v1 Announce Type: new 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.
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.
Artificial Intelligence (cs.AI); Optimization and Control (math.OC)
arXiv:2607.15532 [cs.AI]
(or arXiv:2607.15532v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.15532 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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