In many scenarios where robots or autonomous systems may be deployed, the capacity to infer and reason about the intentions of other agents can improve the performance or utility of the system. For example, a smart home or assisted living facility is better able to select assistive services to deploy if it understands the goals of the occupants in advance. In this article, we present a framework for reasoning about intentions using probabilistic logic programming. We employ ProbLog, a probabilistic extension to Prolog, to infer the most probable intention given observations of the actions of the agent and sensor readings of important aspects of the environment. We evaluated our model on a domain modeling a smart home. The model achieved 0.75 accuracy at full observability. The model was robust to reduced observability.