When is reasoning from the absence of a consequence to the absence of its antecedent valid?

The Dialectical Method and Elegant Causal Attribution: Proof and Four Modes of Ḥusn al-Taʿlīl

• When a genuine necessary implication connects them
• When the consequence is common but not necessary
• When antecedent and consequent are merely associated
• When the poet adds a conclusion after a simile