Assessing trust in online social networks (OSNs) is critical for many applications such as online marketing and network security. It is a challenging problem, however, due to the difficulties of handling complex social network topologies and conducting accurate assessment in these topologies. To address these challenges, we model trust by proposing the three-valued subjective logic (3VSL) model. 3VSL properly models the uncertainties that exist in trust, thus is able to compute trust in arbitrary graphs. We theoretically prove the capability of 3VSL based on the Dirichlet-Categorical (DC) distribution and its correctness in arbitrary OSN topologies. Based on the 3VSL model, we further design the AssessTrust (AT) algorithm to accurately compute the trust between any two users connected in an OSN. We validate 3VSL against two real-world OSN datasets: Advogato and Pretty Good Privacy (PGP). Experimental results indicate that 3VSL can accurately model the trust between any pair of indirectly connected users in the Advogato and PGP.