SIXTEEN$$_3$$ in Light of Routley Stars

For one of the most well-known many-valued logics FDE, there are several semantics, including the star semantics by Richard Routley and Valerie Routley, the two-valued relational semantics by Michael Dunn and the four-valued semantics by Nuel Belnap. The last semantics inspired Yaroslav Shramko and Heinrich Wansing to introduce the trilattice SIXTEEN\(_3\). In this article, we offer two alternative semantical presentations for SIXTEEN\(_3\), by applying the Routleys’ semantics and the Dunn semantics. Based on our new semantics, we discuss related systems with less truth values, as well as the relation to FDE-based modal logics.