probabilisticlogic

Probabilistic logic is a field at the intersection of logic and probability theory that seeks to represent and reason with knowledge under uncertainty. It extends classical logic by incorporating probabilistic elements, such as attaching probabilities to propositions, rules, or entire theories, and by using structured formalisms that combine statistical inference with symbolic reasoning.

Several major strands dominate the landscape. Probabilistic logic programming uses logic programs with probabilistic facts and rules; under distribution semantics, the probability of a query is the probability that it can be proved given random choices of facts. Well-known systems in this family include ProbLog, PRISM, and the Independent Choice Logic. Another cornerstone is Markov Logic Networks, which attach weights to first-order logic formulas and define a probability distribution over possible worlds via a Markov network, enabling joint probabilistic reasoning with rich relational structure. Probabilistic Soft Logic is a related approach that uses continuous truth values in [0,1] and hinge-loss potentials to provide scalable, approximate inference.

In addition to these, there are probabilistic first-order models, probabilistic programming languages, and various frameworks in statistical relational learning that blend logic with probabilistic reasoning. The field addresses both the semantics of combining logic and probability and the practical challenges of inference and learning in large, relational domains.

Applications span knowledge base completion, information extraction, natural language understanding, robotics and planning, bioinformatics, and other areas where data is uncertain and relational structure is important. Probabilistic logic aims to harness the expressive power of logic while accommodating uncertainty in a principled, interpretable way.