Quantified Markov Logic Networks
This work addresses a modeling gap for researchers and practitioners in probabilistic graphical models, particularly in social network analysis, but it is incremental as it builds directly on existing MLN frameworks.
The paper tackled the limitation of Markov Logic Networks (MLNs) in expressing certain statistical statements, such as those involving influencers in social networks, by introducing quantified MLNs with statistical universal quantifiers. The result showed that standard reasoning tasks in quantified MLNs can be reduced to their MLN counterparts in polynomial time.
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.