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JoshuaZ comments on Church: a language for probabilistic modeling - Less Wrong
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Regarding parenthetical, summaries of that sort would be good.
I'm in general pessimistic that were every going to have a really good approach to handling these sorts of probability calculations because they have some versions that are hard. For example, SAT which is NP-complete can be sort of thought of as trying to get a probability distribution where each event is assigned probability of 0 or 1. This doesn't resemble anything rigorous, more just a general intuition. However, the fact that they think that Church might be used for practical applications does make this look good. Also, I may be too focused on a computational complexity approach to things rather than a more general "this makes this easier to program and understand" approach.
Probabilistic inference in general is NP-hard, but it is not clear that (1) this property holds for the kinds of problems people are interested in and, even if it does, that (2) approximate probabilistic inference is hard for this class of problems. For example, if you believe this paper, probabilistic inference without extreme conditional probabilities is easy.