Abstract: We propose a modeling framework for event data, which excels in small data regime with the ability to incorporate domain knowledge. Our framework will model the intensities of the event starts and ends via a set of first-order temporal logic rules. Using softened representation of temporal relations, and a weighted combination of logic rules, our framework can also deal with uncertainty in event data. Furthermore, many existing point process models can be interpreted as special cases of our framework given simple temporal logic rules. We derive a maximum likelihood estimation procedure for our model, and show that it can lead to accurate predictions when data are sparse and domain knowledge is critical.