Journal of Logic and Computation 35 (7):1-27. 2025What happens if we drop the axiom (K) and the necessitation rule from the usual axiomatic presentation of modal logic T? This system was first introduced by Ivlev (1988, Bull. Sect. Log., 17, 114–121). We show that this logic is a syntactical variant of the well-known paraconsistent logic BK (also known as mbCciw), which belongs to a large family of Brazilian paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Our approach is