  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.
