I'm building an ontology to find peoples' skills. I want to infer that when a person A passed a course B and course B provides skill C, then person A has skill C. Is there a way to do this in Protégé?
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Sure, you're saying that when you have:
A →passed B →providesSkill C
you want to infer that
A →hasSkill C
You can do that with the subproperty chain axiom:
passed • providesSkill ⊑ hasSkill
For a more detailed example of how to add these in Protege, see the (not quite a duplicate) question: Adding statements of knowledge to an OWL Ontology in Protege).

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