How people make inferences about causal systems with multiple potentially interactive causes is an important but complicated question. We conducted an experiment using a blicket detector task with an iterated-learning design to study people's prior beliefs about functional form. Participants observed stimuli and generated predictions based on their observations. Some of these predictions were then observed by the next participants, ultimately converging on answers that reflect only people's prior beliefs. Our results suggest that people make judgments by balancing a preference for simple causal systems against one for adequately explaining the available data. To explain these results, we propose a novel computational model that features a grammar-based prior, expressing causal relationships as compositions of three atomic forms. This model outperformed one that is based on the noisy-OR and captured people's expectations about such causal systems, suggesting the importance of logical operations~---~disjunction, conjunction, and negation~---~in characterizing people's causal knowledge.