 Assume the exclusive cp-law is formulated with the help of a non-strict conditional \(A \rightarrow B\). Drawing correct inferences from non-strict conditionals requires non-classical rules of valid inferences: The non-monotonicity of Default Modus Ponens means formally that although the inference from \(A\rightarrow B\) and \(A(d)\) to \(B(d)\) is correct (i.e., \(A\rightarrow B, A(d) \dproves B(d)\) holds, where ‘\(\dproves\)’ stands for ‘non-monotonically correct inference’), the inference from the extended premise set \(A\rightarrow B, H\rightarrow \neg B, A(d)\), and \(H(d)\) to \(B(d)\) is incorrect (i.e., \(A\rightarrow B\), A\((d), H(d) \dproves B(d))\). These non-monotonic effects are reflected in non-classical rules for inferences from conditionals to conditionals. For example, take the inference from “If \(A\), then \(B\)” to “If \(A\wedge D\), then \(B\)” (monotonicity \(M)\) or from “If \(A\), then \(B\)” and “If \(B\), then \(D\)” to “If \(A\), then \(D\)” (Cut \(C)\). Both inferences are valid for strict (logical or material) conditionals, but they are not generally correct for non-strict conditionals. Only the more cautious inferences from \(A\rightarrow B\) and \(A\rightarrow D\) to \(A\wedge D\rightarrow B\) (cautious monotonicity CM) or from \(A\rightarrow B\) and \(A\wedge B\rightarrow D\) to \(A\rightarrow D\) (Cautious Cut CC) are correct for non-strict conditionals.