We introduce an approach to detecting inconsistencies in large biological networks by using Answer Set Programming (ASP). To this end, we build upon a recently proposed notion of consistency between biochemical/genetic reactions and high-throughput profiles of cell activity. We then present an approach based on ASP to check the consistency of large-scale data sets. Moreover, we extend this methodology to provide explanations for inconsistencies by determining minimal representations of conflicts. In practice, this can be used to identify unreliable data or to indicate missing reactions.