ad 1: why not attach a credibility score to relations (probably aggregated from multiple sources) and query against those too?
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What inference rules for unreliable data do you suggest?
Probabalistic Soft Logic, Markov Logic, Natural Soft Logic (https://youtu.be/EX1hKxePxkk?t=23m00s). Despite those operate on the semantic level to credit/discredit drawn inferences and treat phrases at face value, I assume you can factor in credibility from sources as well.
is there something wrong with inductive logic?
https://en.wikipedia.org/wiki/Inductive_reasoning
Inductive logic needs an implementation. These are things like Bayes Nets, Inference using Gibbs sampling, PSL, etc.
You can sorta, mostly get them to work if you have a clean graph, and are prepared to spend a long time debugging.
The problem is that no one has managed to get them to work well enough to be useful on dirty, web-scale knowledge graphs.