# A Fundamental Probabilistic Fuzzy Logic Framework Suitable for Causal Reasoning

arXiv: https://arxiv.org/abs/2205.15016 · HTML: https://mlsanity.com/paper/2205.15016/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 2 of 2)

- [Fast and Slow Learning of Recurrent Independent Mechanisms](https://mlsanity.com/paper/2105.08710/) (2021)
- [Review of The Book of Why: The New Science of Cause and Effect](https://mlsanity.com/paper/2003.11635/) (2020)

## Built on by (most cited first, 3 of 3)

- [The Odyssey of Commonsense Causality: From Foundational Benchmarks to Cutting-Edge Reasoning](https://mlsanity.com/paper/2406.19307/) (2024)
- [Integrating Fuzzy Logic with Causal Inference: Enhancing the Pearl and Neyman-Rubin Methodologies](https://mlsanity.com/paper/2406.13731/) (2024)
- [FRoG: Evaluating Fuzzy Reasoning of Generalized Quantifiers in Large Language Models](https://mlsanity.com/paper/2407.01046/) (2024)

## Abstract (arXiv)

In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy attribute. To do so, we associate some specific crisp random variables to the random experiment. Then, several formulas are presented, which make it easier to compute different conditional probabilities and expected values of these random variables. Also, we provide measure theoretical basis for our probabilistic fuzzy logic framework. Note that in our theory, the probability density functions of continuous distributions which come from the aforementioned random variables include the Dirac delta function as a term. Further, we introduce an application of our theory in Causal Inference.