The Semantic Web technology should enable publishing of numerous resources of scientific and other, highly formalized data on the Web. The application of mining these huge, networked Web repositories seems interesting and challenging. In this paper we present and discuss an inductive reasoning procedure for mining frequent patterns from the knowledge bases represented in OWL DLP. OWL DLP, also known as Description Logic Programs, lies at the intersection of the expressivity of OWL DL and Logic Programming. Our method is based on a special trie data structure inspired by similar, efficient structures used in classical and relational data mining settings. Conjunctive queries to OWL DLP knowledge bases are the language of frequent patterns.