I understand that RDF* solves the issue of properties and attributes and internal structure missing in RDF. But I wonder what are some use cases when RDF* are better than LPG? And what are the main advantages of RDF* over LPGs?
What are the key advantages and use cases of RDF* graphs compared to LPG?
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There are multiple use cases that, with the introduction of the RDF* (RDF Star) framework, RDF* can compete with LPG applications according to this OpenCredo blog.
Being able to serve as a framework to support a use case does not alone merit an "advantage", but it does introduce the benefits that RDF already had to a new use case.
(I am answering under the assumption that you are distinguishing the existing use cases where RDF (without *) was already more ideal than LPG, from the use cases that were better suited for LPG before the introduction of RDF Star. This is why I omitted "Application with Cross-Domain Knowledge" from the above list since that use case was merely enhanced as an even better RDF choice.)