Hi Tim,
These are path expressions, not inferences - so they are not materialized. ^edg:activityOf is simply an inverse path - the actual triple is :BusActivity edg:activityOf :BusFunction
You can query for these in SPARQL as you would for any triple pattern. Sequential paths can also be queried for in a long form or in a short form using path expressions.
In GraphQL, you can query for them using the name of the property shape with the inverse path or any other path - as if it actually existed e.g., you will see businessActivities link when constructing a GraphQL query for business functions
If you want to materialize these triples, you could use SPIN or SHACL rules to define and generate inferences. You would need to use the actual new predicates to do so e.g., :BusActivity edg:activityOf :BusFunction could generate :BusFunction edg:busActivities :BusActivity. These rules could be then ran using using the Transform tab or (in 7.0) Inference panel and/or the Export tab for RDF export.