Ontology design is a complex and time-consuming process. It is extremely difficult for human experts to discover ontology from given data or texts. This paper presents a semi-automatic method for ontology extraction and design. The method is based on Formal Concept Analysis and a Horn clause model of a concept lattice. Inputs to the technique are domain-specific texts or data. After transformations, resulting domain-specific ontology is represented as a set of rules and facts according to Horn clause model of concept lattice based ontology representation. Ontology designer is given this initial ontology expression for further extension by adding concepts and relationships (part-of, related to, etc) by using a rule language based on Horn clauses. Validation of ontology is done by logical inference.