Simply by adding reflexivity of the accessibility relation \(\mathcal{R}\) to the conditions for a model in Section 3.1, one gains the validity of \(t{:}X \rightarrow X\) for every \(t\) and \(X\), and obtains a semantics for \(\mathsf{JT}\), the justification logic analog of the modal logic \({\textsf{T}}\), the weakest logic of knowledge. Indeed, if \({\mathcal{M},\Gamma{\Vdash}t{:}X}\) then, in particular, \(X\) is true at every state accessible from \(\Gamma\). Since the accessibility relation is required to be reflexive, \({\mathcal{M},\Gamma{\Vdash}X}\). Weak and strong completeness theorems are provable using the same machinery that applied in the case of \(\textsf{J}\), and a semantic proof of a Realization Theorem connecting  \(\mathsf{JT}\) and \({\textsf{T}}\) is also available. The same applies to the logics discussed below.