[2] It is applicable to a variety of machine learning problems, such as collective classification, entity resolution, link prediction, and ontology alignment.

PSL combines two tools: first-order logic, with its ability to succinctly represent complex phenomena, and probabilistic graphical models, which capture the uncertainty and incompleteness inherent in real-world knowledge.

PSL provides sophisticated inference techniques for finding the most likely answer (i.e. the maximum a posteriori (MAP) state).

The SRL community has introduced multiple approaches that combine graphical models and first-order logic to allow the development of complex probabilistic models with relational structures.

A notable example of such approaches is Markov logic networks (MLNs).

[3] Like MLNs, PSL is a modelling language (with an accompanying implementation[4]) for learning and predicting in relational domains.

Unlike MLNs, PSL uses soft truth values for predicates in an interval between [0,1].

This allows for the underlying inference to be solved quickly as a convex optimization problem.

This is useful in problems such as collective classification, link prediction, social network modelling, and object identification/entity resolution/record linkage.

Probabilistic Soft Logic was first released in 2009 by Lise Getoor and Matthias Broecheler.

Later versions of PSL would still keep the ability to reason about similarities, but generalize the language to be more expressive.

In 2017, a Journal of Machine Learning Research article detailing PSL and the underlying graphical model was published along with the release of a new major version of PSL (2.0.0).

[2] The major new features in PSL 2.0.0 was a new type of rule mainly used in specifying constraints and a command-line interface.

A PSL model is composed of a series of weighted rules and constraints.

Restricting each side to a linear combination ensures that the resulting potential is convex.

This type of rule is especially useful for collective classification problems, where only one class can be selected.

A PSL program defines a family of probabilistic graphical models that are parameterized by data.

More specifically, the family of graphical models it defines belongs to a special class of Markov random field known as a Hinge-Loss Markov Field (HL-MRF).

An HL-MRF determines a density function over a set of continuous variables

This density is a logarithmically convex function, and thus the common inference task in PSL of finding a maximum a posteriori estimation of the joint state of

If a predicate is labeled as open, then PSL does not make the closed-world assumption.

Data is used to instantiate several potential functions in a process called grounding.

Grounding predicates in PSL is the process of making all possible substitutions of the variables in each predicate with the existing constants in the data, resulting in a collection of ground atoms,

Each of the ground rules are interpreted as either potentials or hard constraints in the induced HL-MRF.

A ground logical rule is transformed into its disjunctive normal form.

be the set of indices of the variables that correspond to atoms that are not negated, and, likewise

the set of indices corresponding to atoms that are negated, in the disjunctive clause.

[7] It supports all the features commonly used in a reproducible form that does not require compilation.

Below is a toy example from this repository that can be used to infer relations in a social network.

Along with each rule is a comment describing the motivating intuition behind the statements.