What are the advantages of LePUS3 over UML?

When searching online for object oriented concepts such as the composite design pattern I often found them represented in the LePUS3 notation. I am not really familiar with this modeling language.

Is it something I should prefer over UML?

LePUS3 was designed to be an improvement over other modeling languages and is specifically designed to be an enhancement to UML. The benefits of LePUS3 are laid out in the paper that introduced it, and you can see a summary of these benefits on the preview of the scientific paper show at the link.

I'll reproduce the paper's stated advantages here:

• Rigour. LePUS3 is a logic visual language: a chart stands for a formula in an axiomatized theory in the classical first-order predicate calculus.
• Parsimony & scalability. LePUS3 offers powerful abstractions: charts scale well and do not clutter with the size of the program.
• Minimality. LePUS3 vocabulary is minimal, consisting of 15 tokens.
• Decidability & verifiability. Consistency between a given specification (a chart) and an implementation (a Java program) can be verified by a button-click.
• Program Visualization. Charts modeling Java programs can be reverse-engineered from source code.