MOTIVATION: Network-based driver identification methods that can exploit mutual exclusivity typically fail to detect rare drivers because of their statistical rigor. Propagation-based methods in contrast allow recovering rare driver genes, but the interplay between network topology and high-scoring nodes often results in spurious predictions. The specificity of driver gene detection can be improved by taking into account both gene-specific and gene-set properties. Combining these requires a formalism that can adjust gene-set properties depending on the exact network context within which a gene is analyzed. RESULTS: We developed OMEN: a logic programming framework based on random walk semantics. OMEN presents a number of novel concepts. In particular, its design is unique in that it presents an effective approach to combine both gene-specific driver properties and gene-set properties, and includes a novel method to avoid restrictive, a priori filtering of genes by exploiting the gene-set property of mutual exclusivity, expressed in terms of the functional impact scores of mutations, rather than in terms of simple binary mutation calls. Applying OMEN to a benchmark dataset derived from TCGA illustrates how OMEN is able to robustly identify driver genes and modules of driver genes as proxies of driver pathways. AVAILABILITY AND IMPLEMENTATION: The source code is freely available for download at www.github.com/DriesVanDaele/OMEN. The dataset is archived at https://doi.org/10.5281/zenodo.6419097 and the code at https://doi.org/10.5281/zenodo.6419764. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.