 There are logics that are not equivalential but have the property of having a set of formulas \([p \Rightarrow q]\) which collectively behave in a very weak sense as the implication \(\rightarrow\) does in many logics. Namely, that has the properties \((\tR_{\Delta})\) and \((\tMP_{\Delta})\) in the syntactic characterization of a set of equivalence formulas, i.e.,