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I hadn't even heard of Probabilistic Logic before today. My world view was already leaning in this direction as I never really put much stock in either the law of the excluded middle or the principal of bivalence, and I've already been thinking that truth values made more sense if treated like quantum probabilities.
What's a Good Introduction/Summary to Probabilistic Logic?
You can start with SEP's entries : Logic and Probability and Quantum Logic and Probability Theory.
Both have a Bibliography.
