Ontologies play a key role in agent communication and the emerging Semantic Web to define a vocabulary of concepts and their relationships. Different agents and web services may use vocabularies from different ontologies to describe their data. The current research on ontology mapping and ontology translation mainly focuses on how to map and translate vocabularies and associated data instances from one ontology to another. However, more complicated true statements, such as axioms (rules), are used or being developed to describe the relationships among the concepts. When extending one ontology using complicated true statements (theory) from another, we must confront the problem of theory translation, which is difficult because of the asymmetry of translation. In this paper, using an inferential approach we call axiom derivation, we show how to translate complex axioms between different time ontologies. We also prove the validity of our algorithm.