ProbLog vs Markov Logic Networks: Probabilistic Logic Programming vs Statistical Relational Learning

ProbLog excels at exact, query-driven probabilistic inference because it extends Prolog's proof procedure with a reduction to weighted model counting. For example, in biological network analysis tasks like link prediction on the YEAST dataset, ProbLog can compute exact marginal probabilities for specific queries, providing mathematically precise results when the knowledge base is well-structured and the query space is focused.

Markov Logic Networks (MLNs) take a fundamentally different approach by constructing an undirected graphical model from weighted first-order logic formulas. This results in a joint probability distribution over all possible worlds, enabling global reasoning across the entire domain. The trade-off is that inference becomes intractable for large domains, requiring approximate methods like MC-SAT or lifted belief propagation, which can achieve 80-90% accuracy on benchmark tasks like collective classification in Cora but without the exactness guarantees ProbLog provides for its query scope.

The key trade-off: If your priority is exact, explainable inference over discrete relational data with specific queries—such as medical diagnosis or legal reasoning—choose ProbLog. If you prioritize learning weights from noisy, incomplete data and performing global inference across all entities simultaneously—such as entity resolution or social network analysis—choose Markov Logic Networks. Consider ProbLog when interpretability and precision are non-negotiable; choose MLNs when scalability and weight learning from real-world data are paramount.

ProbLog excels at exact, explainable inference over discrete relational domains because its proof-procedure-based semantics provide a direct logical trace for every query. For example, in a biological network analysis task, ProbLog can compute the exact probability of a gene being activated given a set of probabilistic regulatory rules, offering a transparent chain of reasoning that is auditable by domain experts. This makes it the superior choice when the knowledge base is well-structured, the domain is finite, and the cost of an incorrect inference—such as in medical diagnosis or safety-critical systems—is extremely high.

Markov Logic Networks (MLNs) take a fundamentally different approach by compiling first-order logic into an undirected graphical model, enabling weight learning from data and approximate inference at scale. This results in a critical trade-off: MLNs can handle noisy, ambiguous data and learn rule weights automatically from training examples, which ProbLog's explicit probability labeling cannot do natively. For instance, in a large-scale entity resolution task across millions of records, an MLN can learn the relative importance of different matching rules, whereas ProbLog would require a manually specified, fully ground model that may become computationally intractable.

The key trade-off: If your priority is interpretability, exactness, and reasoning over a closed-world knowledge base, choose ProbLog. Its proof-based inference provides a defensible audit trail essential for regulatory compliance. If you prioritize scalability, learning from data, and handling noisy open-world domains, choose Markov Logic Networks. The graphical model approach, while often approximate, is the pragmatic path when the rules themselves are uncertain and must be induced from data. Consider a hybrid stack where ProbLog serves as the verifiable reasoning core for high-stakes decisions, while MLNs handle the messy, large-scale weight learning from unstructured corpora.