First order logic lies at the core of many methods in mathematics, philosophy, linguistics, and computer science. Although important efforts have been made to extend first order logic to the task of handling uncertainty, there is still a lack of a consistent and unified approach, especially within the Dempster-Shafer (DS) theory framework. In this work we introduce a systematic approach for building belief assignments based on first order logic formulas. Furthermore, we outline the foundations of Uncertain Logic, a robust framework for inference and modeling when information is available in the form of first order logic formulas subject to uncertainty. Applications include data fusion, rule mining, credibility estimation, and crowd sourcing, among many others.
@inproceedings{nunezetal13folinds,
title={Modeling Uncertainty in First-Order Logic: A Dempster-Shafer Theoretic Approach},
author={Rafael C. Núñez and Matthias Scheutz and Kamal Premaratne and Manohar N. Murthi},
year={2013},
booktitle={8th International Symposium on Imprecise Probability: Theories and Applications},
url={https://hrilab.tufts.edu/publications/nunezetal13folinds.pdf}
}