 However, there are good grounds for thinking that a system of nonmonotonic logic should fail to include a generalized deduction theorem. The very nature of defeasible consequence ensures that it must be so. Consider, for example, the left-to-right direction: suppose that \(\Gamma \cup \{p\} \dproves q\). Should it follow that \(\Gamma \dproves (p \Rightarrow q)\)? Not at all. It may be that, normally, if \(p\) then \(\neg q\), but \(\Gamma\) may contain defaults and information that defeat and override this inference. For instance, it might contain the fact \(r\) and the default \(((r \amp p) \Rightarrow q)\). Similarly, consider the right-to-left direction: suppose that \(\Gamma \dproves (p \Rightarrow q)\). Should it follow that \(\Gamma \cup \{p\} \dproves q\)? Again, clearly not. \(\Gamma\) might contain both \(r\) and a default \(((p \amp r) \Rightarrow \neg q)\), in which case \(\Gamma \cup \{p\} \dproves \neg q\).