On the Semantic Relationship between Probabilistic Soft Logic and Markov Logic

TL;DR

This paper clarifies the semantic relationship between Probabilistic Soft Logic (PSL) and Markov Logic Networks (MLN) by extending fuzzy logic to include weights, revealing their conceptual connection.

Contribution

It formally relates PSL and MLN through a logical perspective by extending fuzzy logic with weights, showing PSL as a generalization of MLN in a many-valued context.

Findings

PSL's weight scheme generalizes MLN's in a many-valued setting

The relationship between PSL and MLN parallels fuzzy and Boolean logic

A formal semantic connection between PSL and MLN is established

Abstract

Markov Logic Networks (MLN) and Probabilistic Soft Logic (PSL) are widely applied formalisms in Statistical Relational Learning, an emerging area in Artificial Intelligence that is concerned with combining logical and statistical AI. Despite their resemblance, the relationship has not been formally stated. In this paper, we describe the precise semantic relationship between them from a logical perspective. This is facilitated by first extending fuzzy logic to allow weights, which can be also viewed as a generalization of PSL, and then relate that generalization to MLN. We observe that the relationship between PSL and MLN is analogous to the known relationship between fuzzy logic and Boolean logic, and furthermore the weight scheme of PSL is essentially a generalization of the weight scheme of MLN for the many-valued setting.