 Truthmaker semantics can be seen from a (multi)modal perspective (van Benthem 1989), since a state model \({\langle S, \sqsubseteq, V \rangle}\) can be understood as a modal information logic, and thus can be described by modal languages. One interesting possibility (van Benthem 2018: Section 13) starts by taking two modalities, \(\langle\sqsubseteq\rangle\varphi\) and \(\langle\sqsupseteq\rangle\varphi\), whose semantic interpretation is given in the standard modal way, with the first modality relying on the partial order \(\sqsubseteq\), and the second relying on its converse  \(\sqsupseteq\).[20]  Then, one can add a (binary) modality describing least upper bound