Designing ontologies and specifying axioms of the described domains is an expensive and error-prone task. Thus, we propose a method originating from Formal Concept Analysis which uses empirical data to systematically generate hypothetical axioms about the domain, which are represented to an ontology engineer for decision.In this paper, we focus on axioms that can be expressed as entailment statements in the description logic ({mathcal{F!LE}}). The proposed technique is an incremental one, therefore, in every new step we have to reuse the axiomatic information acquired so far. We present a sound and complete deduction calculus for ({mathcal{F!LE}}) entailment statements.We give a detailed description of this multistep algorithm including a technique called empirical attribute reduction and demonstrate the proposed technique using an example from mathematics.We give a completeness result on the explored information and address the question of algorithm termination. Finally, we discuss possible applications of our method.