These were some of the major projects: https://homes.cs.washington.edu/~suciu/project-mystiq.html, http://maybms.sourceforge.net/, http://infolab.stanford.edu/trio/, http://www.cs.umd.edu/~amol/PrDB/, http://dl.acm.org/citation.cfm?id=1376686.
I thought BlinkDB was data warehousing on hdfs? I dont see any mention of inference-like features in the docs?
Although some terms come up in both places (e.g., confidence bounds, noise, etc), BlinkDB and probabilistic databases are fundamentally different from each other (I have worked on both topics).
I hadn't heard about DeepDive until now, but I did previously come across another project that does probabilistic reasoning: http://alchemy.cs.washington.edu. I cannot speak to how they compare since I haven't looked into either in great depth yet.
There is a lot of work on probabilistic inference. Huge volumes.
But then if you are interested on papers on using probabilistic inference on unstructured information there is a lot less information.
If you are looking for actual implementation reports there isn't much. The most interesting are the previously mentioned Probase paper, The Google Knowledge Graph paper and assorted IBM Watson stuff.
I've just realised that DeepDive is also the Wisci project[1], which is something I've been watching for a while
That Alchemy implementation requires a structured database of information, and doesn't really deal with how to get that.
You're talking about the work that Prof. Daisy Zhe Wang and her students are doing over at the DSR lab. Go gators!
So many open source "Knowledge Graph"-y type projects concentrate on building them like databases, with a query language that assumes the data in them is correct. You see this in things like Freebase, DBPedia and Wikidata, where they typically end up in a triple store and you query using SPARQL.
This isn't how the real world works, and there isn't a lot of publicly available software that takes this into account. There aren't even than many papers about it (the Microsoft Probase paper is one, and there is work from Florida University(?) about using Markov chains to reason while taking probabilities into about).
I'm excited to take a look at this.
[1] http://deepdive.stanford.edu/doc/general/inference.html