With the growing number of published functional magnetic resonance imaging (fMRI) studies, meta-analysis databases and models have become an integral part of brain mapping research. Coordinate-based meta-analysis (CBMA) databases are built by extracting both coordinates of reported peak activations and term associations using natural language processing techniques from neuroimaging studies. Solving term-based queries on these databases makes it possible to obtain statistical maps of the brain related to specific cognitive processes. However, existing tools for analysing CBMA data are limited in their expressivity to propositional logic, restricting the variety of their queries. Moreover, with tools like Neurosynth, term-based queries on multiple terms often lead to power failure, because too few studies from the database contribute to the statistical estimations. We design a probabilistic domain-specific language (DSL) standing on Datalog and one of its probabilistic extensions, CP-Logic, for expressing and solving complex logic-based queries. We show how CBMA databases can be encoded as probabilistic programs. Using the joint distribution of their Bayesian network translation, we show that solutions of queries on these programs compute the right probability distributions of voxel activations. We explain how recent lifted query processing algorithms make it possible to scale to the size of large neuroimaging data, where knowledge compilation techniques fail to solve queries fast enough for practical applications. Finally, we introduce a method for relating studies to terms probabilistically, leading to better solutions for two-term conjunctive queries (CQs) on smaller databases. We demonstrate results for two-term CQs, both on simulated meta-analysis databases and on the widely used Neurosynth database.