Subjective Logic (SL) is a type of probabilistic logic, which is suitable for reasoning about situations with uncertainty and incomplete knowledge. In recent years, SL has drawn a significant amount of attention from the multi-agent systems community as it connects beliefs and uncertainty in propositions to a rigorous statistical characterization via Dirichlet distributions. However, one serious limitation of SL is that the belief updates are done only based on completely observable evidence. This work extends SL to incorporate belief updates from partially observable evidence. Normally, the belief updates in SL presume that the current evidence for a proposition points to only one of its mutually exclusive attribute states. Instead, this work considers that the current attribute state may not be completely observable, and instead, one is only able to obtain a measurement that is statistically related to this state. In other words, the SL belief is updated based upon the likelihood that one of the attributes was observed. The paper then illustrates properties of the partial observable updates as a function of the state likelihood and illustrates the use of these likelihoods for a trust estimation application. Finally, the utility of the partial observable updates is demonstrated via various simulations including the trust estimation case.