Logical Credal Networks

Radu Marinescu, Haifeng Qian, Alexander G. Gray, Debarun Bhattacharjya, Francisco Barahona, Tian Gao, Ryan Riegel, Pravinda Sahu

Keywords: graphical models, probabilistic logic, knowledge representation, bayesian networks

TL;DR: We introduce a new probabilistic logic that allows probability bounds on logic formulas and independence relations between their atoms.

Abstract: We introduce Logical Credal Networks (or LCNs for short) -- an expressive probabilistic logic that generalizes prior formalisms that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds on logic formulas, an LCN specifies a set of probability distributions over all its interpretations. Our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. We also define a generalized Markov condition that allows us to identify implicit independence relations between atomic formulas. We evaluate our method on benchmark problems such as random networks, Mastermind games with uncertainty and credit card fraud detection. Our results show that the LCN outperforms existing approaches; its advantage lies in aggregating multiple sources of imprecise information.