 Since every non-trivial system of connexive logic in the vocabulary of classical logic has to omit some classical tautologies, and since the standard paradoxes of non-relevant, material implication can be avoided by rejecting Conjunctive Simplification, i.e., (A ∧ B) → A and (A ∧ B) → B, Routley requires for a connexive logic the rejection or qualification of Conjunctive Simplification (or equivalent schemata). Although according to Routley (1978, Routley et al. 1982) and Routley and Routley (1985) the idea of negation as cancellation, see sections 3.3 and 4.3., motivates both the failure of Conjunctive Simplification and AT’ and BT, the model-theoretic semantics for connexive logics developed in Routley 1978, see section 4.2, makes use of what has later come to be known as the Routley star negation, see the entry on  negation.