In many logical rule-based systems, it often happens that opposite statements can be concluded, hence superiorities (or priorities) among rules are needed to solve such conflicts. Since the specific circumstances describing the scenario at hand determine which rules may apply, we thus need a mechanism able to compute such superiorities dynamically, case-by-case. We formalise a non-monotonic logic able to dynamically compute superiorities over rules. Finally, we advance efficient algorithms to compute the (positive and negative) conclusions of such theories, and prove their computational properties.