In this paper, we explore a new approach to negation in the operational semantics for relevant logic. Urquhart’s seminal semilattice frame semantics does not validate all the negation principles of relevant logic R, notably Contraposition. We introduce a logic that validates Contraposition at the expense of Contraction, reflecting their incompatibility in operational semantics. Three different types of frames for this non-contractive yet contrapositive logic are presented. (1) Contrapositive frame, which slightly modifies Urquhart’s original semilattice frame. (2) Functional multiset-multiset (FMM) frame, adapting Standefer’s functional set frame which has proven equivalent to the semilattice frame for the positive fragment. (3) Bi-operational frame that incorporates dual binary operations, serving as a bridge between contrapositive frames and FMM frames. We demonstrate that these three frame types are equivalent, allowing for isomorphic transformations among them. The paper concludes by presenting a labeled sequent calculus for this logic.