Properties are "on the fly" when they're used for a single application, not made to be reusable anywhere else. An example of an on the fly property can be found in CurriedFunction, where we see the following for the statement "Chicago is between Los Angeles and New York":
:Chicago :betweenProperty :chicagoBetween. :NewYork :chicagoBetween :LosAngeles.
The on-the-fly property there is :chicagoBetween.
Etna'Rosso argued on #swig that this is an anti-pattern because predicates in RDF are Tbox elements rather than Abox elements. That claim makes little sense to DanConnolly; there's no Tbox nor Abox in the RDF model-theoretic semantics. SeanPalmer believes that the description of Tbox and Abox on Wikipedia matches the design of vocabularies and instance data as implemented by RDF Schema/OWL, and should document why in use cases.
:NewYork [ :between :Chicago ] :LosAngeles.