 One difference between their systems is that Cooper defines validity relative to trivalent valuations that are atom-classical; another is that Cooper uses so-called quasi-conjunction and disjunction (see below), whereas Olkhovikov and Cantwell use the common min and max rules for conjunction and disjunction, respectively. For Cooper and Cantwell, in particular, and similarly for Belnap (1973), a central motivation for this conditional is the validation of the principle of Negation Commutation for the conditional, namely the conjunction of: