Quantified Markov Logic Networks

TL;DR

This paper introduces quantified Markov Logic Networks, extending MLNs with universal quantifiers to express more complex statistical statements, and shows that inference tasks can be efficiently reduced to standard MLN inference.

Contribution

It proposes quantified MLNs with universal quantifiers and demonstrates polynomial-time reductions for key inference tasks, enhancing MLN expressiveness.

Findings

Quantified MLNs can express complex statistical statements.

Inference tasks in quantified MLNs reduce to standard MLN inference in polynomial time.

The approach broadens the applicability of MLNs in statistical modeling.

Abstract

Markov Logic Networks (MLNs) are well-suited for expressing statistics such as "with high probability a smoker knows another smoker" but not for expressing statements such as "there is a smoker who knows most other smokers", which is necessary for modeling, e.g. influencers in social networks. To overcome this shortcoming, we study quantified MLNs which generalize MLNs by introducing statistical universal quantifiers, allowing to express also the latter type of statistics in a principled way. Our main technical contribution is to show that the standard reasoning tasks in quantified MLNs, maximum a posteriori and marginal inference, can be reduced to their respective MLN counterparts in polynomial time.