Model-complete text comprehension aims at interpreting a natural language text with respect to a semantic domain model describing the classes and their properties relevant for the domain in question. Solving this task can be approached as a structured prediction problem, consisting in inferring the most probable instance of the semantic model given the text. In this work, we focus on the challenging sub-problem of cardinality prediction that consists in predicting the number of distinct individuals of each class in the semantic model. We show that cardinality prediction can successfully be approached by modeling the overall task as a joint inference problem, predicting the number of individuals of certain classes while at the same time extracting their properties. We approach this task with probabilistic graphical models computing the maximum-a-posteriori instance of the semantic model. Our main contribution lies on the empirical investigation and analysis of different approximative inference strategies based on Gibbs sampling. We present and evaluate our models on the task of extracting key parameters from scientific full text articles describing pre-clinical studies in the domain of spinal cord injury.