Logical Credal Networks

TL;DR

Logical Credal Networks provide a flexible probabilistic logic framework that handles imprecise information and combines features of propositional and first-order logic with Markov properties, enabling effective inference in complex real-world tasks.

Contribution

This paper introduces Logical Credal Networks, a novel probabilistic logic model that unifies logic and probability with imprecise information handling and Markov properties, without restrictive assumptions.

Findings

Outperforms existing methods in MAP inference tasks.

Effectively aggregates multiple sources of imprecise information.

Successfully applied to Mastermind and credit card fraud detection.

Abstract

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.