Can Bayesian inference be combined with knowledge-based systems? I've been struggling with the connection between knowledge-based AI systems and Bayesian inference for a while now. While I continue to sweep through the literature, I would be happy if someone can answer these more specific questions directly

Are Bayesian inference based methods used in reasoning or Q/A systems -- to arrive at conclusions about questions whose answers are not directly present in the knowledge base?

In other words, if a Q/A system doesn't find an answer in a knowledge base, can it use Bayesian inference to use the available facts to suggest answers with varying likelihoods?

If yes, could you point me to some implementations?
Yes, it is possible to combine probabilistic / bayesian reasoning and a traditional "knowledgebase".  And some work along those lines has been done.  See, for example, ProbLog ("Probabilistic Prolog") which combines logic programming and probabilistic elements.  See:  

https://dtai.cs.kuleuven.be/problog/tutorial/mpe/01_bn.html

Another project to look at is Pr-OWL
 ("Probabilistic OWL") which adds Bayesian reasoning to the Semantic Web stack.

Of course neither of these deals specifically with QA systems, but both represent some work on at least the foundational aspect of combining traditional logic and/or ontologies, with probabilistic approaches.  Building a QA system on top of that is an exercise for the reader...