One important question that arises when dealing with temporal databases in context of object-oriented systems is the method that associates time with attributes relationship semantics. Results of previous work about attribute versioning, particularity extending flat(First Normal Form: FNF) or nested(Non-First Normal Form: NFNF) relational models. are not applicable to temporal object-oriented databases. This is because object-oriented models provide more powerful constructs than traditional models for structuring complex objects. Therefore, this paper presents an formal approach for incorporating temporal extension to object-oriented databases. Our goal in this paper is to study temporal object-oriented database representation according to generalization, aggregation and association among objects. We define tile concepts of attribute versioning in temporal object-oriented model, and we concentrate on the representation of temporal relationship among objects. Another contribution of this paper is to specify time constraints on relationship semantics and analyze our model based on representation criteria. By means of formalizing tile temporal object oriented model, this paper can not only provide tile robust operating functions that design algebraic operators, but also entrance the reuse of modules.