Why another general purpose search engine? How about a niche, for example a search engine that can be extensively controlled by using Boolean algebra, Regex, first-order logic?
Googles results got less and less reasonable over the last years.
Grep through your HD. How fast? Now imagine grepping through the internetz.
As for FOLogic, IIRC RDF was related to that (or was that, can't remember) and it takes the sites investment to get that working on their site ie. you can't expect formal relationships between objects to appear magically, someone has to do it. And FOL if it existed may be computationally expensive.
And once you've got all that, how easy would it be to use? Probably most would go back to keyword searches.
Googles results got less and less reasonable over the last years.