<p>In this paper, we introduce two new semantic presentations of Abelian logic, the non-trivial negation inconsistent logic of Abelian lattice-ordered groups, which was independently developed by Ettore Casari, and by Robert Meyer and John Slaney. Abelian logic is presented through a methodology that combines elements of what is sometimes referred to as the “Bochum Plan” and the “American Plan.” While the Bochum Plan is an approach to defining contra-classical logics, the American Plan-developed by Nuel Belnap and Michael Dunn-in particular offers a conception of negation that invites an application of the Bochum Plan. The first semantics is a ternary frame Kripke semantics, and the second is based on ideas from Edwin Mares’ work. Thereby emerges a condition for the falsity of Abelian implication to be supported, which we analyse further in the separate context of the first-degree entailment logic. The perspectives are united in the end to provide a defence against the scepticism concerning the status of the Abelian negation as a negation.</p>