# Logic, Optimization, and Artificial Intelligence

arXiv: https://arxiv.org/abs/2607.15532 · HTML: https://mlsanity.com/paper/2607.15532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 129 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [Clingo goes Linear Constraints over Reals and Integers](https://mlsanity.com/paper/1707.04053/) (2017)
- [Taking Principles Seriously: A Hybrid Approach to Value Alignment](https://mlsanity.com/paper/2012.11705/) (2020)
- [Constraint Answer Set Programming: Integrational and Translational (or SMT-based) Approaches](https://mlsanity.com/paper/2107.08252/) (2021)
- [Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories](https://mlsanity.com/paper/1606.07860/) (2016)
- [Causality from Bottom to Top: A Survey](https://mlsanity.com/paper/2403.11219/) (2024)
- [Logical Credal Networks](https://mlsanity.com/paper/2109.12240/) (2021)
- [An Introduction to Logics of Knowledge and Belief](https://mlsanity.com/paper/1503.00806/) (2015)
- [A Survey of Satisfiability Modulo Theory](https://mlsanity.com/paper/1606.04786/) (2016)
- [Exact and approximate inference in graphical models: variable elimination and beyond](https://mlsanity.com/paper/1506.08544/) (2015)
- [Markov Conditions and Factorization in Logical Credal Networks](https://mlsanity.com/paper/2302.14146/) (2023)
- [Maximum a Posteriori Inference for Factor Graphs via Benders' Decomposition](https://mlsanity.com/paper/2410.19131/) (2024)
- [System ASPMT2SMT:Computing ASPMT Theories by SMT Solvers](https://mlsanity.com/paper/2506.10708/) (2025)

## Abstract (arXiv)

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.