WARNING is no good reason for stopping a flow, but it's a heads up if any other issue happens later.
CRITICAL should be the most alarming log you're ever going to receive, it should be a good excuse to wake you up at 3 am to resolve.
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R. White, and J. Huang. Proceedings of the 33rd International ACM SIGIR Conference on Research and Development in Information Retrieval, page 587--594. New York, NY, USA, ACM, (2010)