 A more regular semantics for extensions of the basic relevance logic B (not to be confused with the truth valued read as “both true and false”) by either AT′ or BT has been presented in Brady 1989. In this semantics, conjunction is defined in the standard way, and there is a non-empty subset of worlds O ⊆ K. The set O contains the distinguished element T used to define truth in a model. The extended model structures contain a function ℑ that maps sets of worlds, and in particular, interpretations of formulas (alias propositions) I(A) to sets of worlds in such a way that a formula A is true at a world t iff t ∈ ℑ(I(A)). This allows Brady to state model conditions capturing AT′ and BT as follows: