 An early and plausible suggestion for the treatment of logical subtraction was made in Hudson (1975). According to this suggestion, no new connective is required, at least if we already have a reasonable implication connective at our disposal, because if we are to think of φ − ψ as giving us the result of taking away the content of ψ from that of φ, then this should be the weakest statement which, together with ψ, has φ as a consequence. But this is just ψ → φ, if the standard natural deduction rules for → from Section  2  are accepted (as in intuitionistic and classical logic). Yet this does not give us the inset equivalence above. If we treat (Sat ∧ Sun) − Sun as Sun → (Sat ∧ Sun), then this is equivalent (in the logics just mentioned and many others) to Sun →  Sat, whereas we wanted the stronger Sat itself (stronger according to those logics, again).