> This problem is known as "attribution" - you have a "no" or "without" in the sentence, but you don't know where it belongs. One could (and one does) argue that the problem cannot be solved with statistical methods (ML), especially not in any domain where accuracy is required, such as medical recored analysis: "no evidence of cancer" and "evidence of no cancer" are very different things.

Couldn't you just parse the sentence into a dependency tree and look at the relationships to figure that out? CoreNLP got both of your examples right (try it at http://nlp.stanford.edu:8080/corenlp/process, can't link the result directly).