Sing and Dance!

Makinson and van der Torre [13] introduce a number of input/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe[19,20] has developed some more I/O logics to include systems without the rule of weakening of the output (or principle of inheritance). We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases−a common form of reasoning. Second, we show how to inject a new (as we call it, “aggregative”) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and completeness theorems for the proposed systems with respect to their intended semantics.