Negation scope detection is widely performed as a supervised learning task which relies upon negation labels at word level. This suffers from two key drawbacks: (1) such granular annotations are costly and (2) highly subjective, since, due to the absence of explicit linguistic resolution rules, human annotators often disagree in the perceived negation scopes. To the best of our knowledge, our work presents the first approach that eliminates the need for world-level negation labels, replacing it instead with document-level sentiment annotations. For this, we present a novel strategy for learning fully interpretable negation rules via weak supervision: we apply reinforcement learning to find a policy that reconstructs negation rules from sentiment predictions at document level. Our experiments demonstrate that our approach for weak supervision can effectively learn negation rules. Furthermore, an out-of-sample evaluation via sentiment analysis reveals consistent improvements (of up to 4.66%) over both a sentiment analysis with (i) no negation handling and (ii) the use of word-level annotations from humans. Moreover, the inferred negation rules are fully interpretable.