Volume 19, Issue 3 (2008), pp. 421–446
It is well known that a formal framework for the schema matching problem (SMP) is important because it facilitates the building of algorithm model and the evaluation of algorithms. An algebraic framework for schema matching is developed in this paper. First, based on universal algebra, we propose a meta-meta structure for schema, which is named multi-labeled schema. This definition has a distinctive feature: it is able to formally describe any particular style of schemas, and transforms a schema and other available information into a finite structure over specific signature. Later, we introduce a formal definition of schema matching that is called multivalent matching. Then, we formulize SMP as a schema homomorphism problem, and prove that SMP is equivalent to finding a semantic homomorphism from one schema to another. These results lead to the main contribution of this paper: an algebraic framework for SMP. This framework builds the algorithm model for SMP. Thirdly, we show a classification of schema matching based on the algebraic framework. Finally, we discuss the relations between matching cardinality and subclasses of schema homomorphism.