Problematic Abstraction

A new show at the New Museum featuring small works by Tomma Abts looks very intriguing. While I have not yet seen the show (but will and soon), the images of the works I have seen (at the New Museum's website and on nytimes.com) show Ms. Abts' interest to lie in representing three-dimensional spaces and hinting at photographic techniques (see elaborate use of "focus" at left). Strangely, the New Museum and the New York Times articles both laud the artist as a true abstractionist and assert that her paintings could be indistinguishable from work made in the 50's or 60's.

Are they bonkers? Though the earlier works in the show are more purely abstract (yet could never be confused with work from the mid-20th century), as the works progress they reference depth via shadow, color and focus in more and more direct ways. Which makes me wonder: what is abstraction exactly? I thought I knew but now I don't. Are illusionistic paintings of three dimensional situations abstract if they depict objects in space like paper cut-outs? Or is abstraction merely a lack of people, places and things, and unrelated to depicting spacial relationships?