There is an algorithm called Constraint Demotion Algorithm (CDA), and its variants, by Tesar & Smolensky 1993, 1998, 2000; Prince & Tesar 2000; Hayes 1999. They were all though in light of the Optimality Theory.
I'm not sure what you mean by "innate". Do you mean "Do UG's claims actually match how people really process language?". To the best of my knowledge, there is no easy way to assess that: I'm not sure one could devise an experiment to validate the UG hypothesis as a whole. Maybe proving or disproving certain claims.
If you mean "Is Generative Grammar a consistent theory?", now that's another story. Even if one could prove it's consistent, it wouldn't necessarily mean it's true, i.e. it successfully accounts for language emergence, evolution, variation, acquisition, etc. in every aspect. If you look at other scientific fields, it seems to me that quantum mechanics AND relativity theory are both consistent models of some aspects of reality. Yet, they are fundamentally irreconcilable. Unless you start unifying them under an overarching model (string theory).
So it all boils down to personal belief, I think, hence the fierce arguments these questions generally spark among linguists.
The issues about UG are closely related to issues about an innate semantics, logic, or methods of reasoning. In the late 1960s, while Chomsky was busy fighting against the Vietnam War, some of his former students developed the heresy of generative semantics.
In 1969, I attended a famous lecture on generative semantics by George Lakoff at the LSA Summer Institute at the University of Illinois. The best part of it was the shouting match during the discussion at the end. Lakoff was standing on stage, wearing a pair of overalls that made him look like a farmer, while Jackendoff was running down the aisle. Everybody enjoyed it, but nobody remembers the details.
In any case, I recently presented a 3-hour tutorial on natural logic, which addresses some of the semantic and psycholinguistic issues. Following are the slides: http://www.jfsowa.com/talks/natlog.pdf