The Peano axioms describe constraints for instances within a set. Is something already "there" just because we can test the constraints after it appears, or use them to make it?
The foundations of OMeta go way way back (starting with Meta II by Val Schorre ca 1964 -- and in the context of the many different approaches to parsing in the 60s). The modern addition to help make OMeta was the packrat parsing idea. It wouldn't be surprising if some Prolog lore wafted its way in, but I don't recall that any of the many parsing schemes that Prolog has been used for were in the conversations. One of the Ur-centers that most parsing theory has to contend with is "Earley Parsing". However, the idea that a dynamic proof can be used to parse goes very far back.