Drug-target interaction studies are important because they can predict drugs' unexpected therapeutic or adverse side effects. In silico predictions of potential interactions are valuable and can focus effort on in vitro experiments. We propose a prediction framework that represents the problem using a bipartite graph of drug-target interactions augmented with drug-drug and target-target similarity measures and makes predictions using probabilistic soft logic (PSL). Using probabilistic rules in PSL, we predict interactions with models based on triad and tetrad structures. We apply (blocking) techniques that make link prediction in PSL more efficient for drug-target interaction prediction. We then perform extensive experimental studies to highlight different aspects of the model and the domain, first comparing the models with different structures and then measuring the effect of the proposed blocking on the prediction performance and efficiency. We demonstrate the importance of rule weight learning in the proposed PSL model and then show that PSL can effectively make use of a variety of similarity measures. We perform an experiment to validate the importance of collective inference and using multiple similarity measures for accurate predictions in contrast to non-collective and single similarity assumptions. Finally, we illustrate that our PSL model achieves state-of-the-art performance with simple, interpretable rules and evaluate our novel predictions using online data sets.