# Logical Credal Networks

arXiv: https://arxiv.org/abs/2109.12240 · HTML: https://mlsanity.com/paper/2109.12240/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 58 references that are in the map.
- First posted on arXiv 25 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Elicitation of Probabilities for Belief Networks: Combining Qualitative and Quantitative Information](https://mlsanity.com/paper/1302.4943/) (2013)
- [Probabilistic Description Logics](https://mlsanity.com/paper/1302.6817/) (2013)
- [Stochastic Logic Programs: Sampling, Inference and Applications](https://mlsanity.com/paper/1301.3846/) (2013)
- [Exploiting Qualitative Knowledge in the Learning of Conditional Probabilities of Bayesian Networks](https://mlsanity.com/paper/1301.3903/) (2013)
- [Consistency Checking and Querying in Probabilistic Databases under Integrity Constraints](https://mlsanity.com/paper/1303.3233/) (2013)

## Built on by (most cited first, 4 of 4)

- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [A Neuro-Symbolic Approach to Multi-Agent RL for Interpretability and Probabilistic Decision Making](https://mlsanity.com/paper/2402.13440/) (2024)
- [Markov Conditions and Factorization in Logical Credal Networks](https://mlsanity.com/paper/2302.14146/) (2023)
- [Logic, Optimization, and Artificial Intelligence](https://mlsanity.com/paper/2607.15532/) (2026)

## Abstract (arXiv)

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds of logic formulas, this logic specifies a set of probability distributions over all interpretations. On the one hand, our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. On the other hand, it has a Markov condition similar to Bayesian networks and Markov random fields that is critical in real-world applications. Having both these properties makes this logic unique, and we investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud. The results show that the proposed method outperforms existing approaches, and its advantage lies in aggregating multiple sources of imprecise information.