5 An Ontology-Composition Algebra Prasenjit Mitra and Gio Wiederhold Stanford University, Stanford CA, 94017, U.S.A., {mitra, gio}@db.stanford.edu Summary. The need for an algebra to manipulate ontologies is motivated by the impossibility of achieving a globally consistent ontology. Our approach is to integrate information from diverse sources by focusing on the intersection of their ontologies and articulating them accordingly. These articulations typically require rules to define semantic correspondences like synonymy, homonymy, hypernymy, overlapping semantics, and abstraction among the terms of interest. The algebra, needed to compose multiple articulations, has to manipulate the ontologies based on these articulation rules. The properties of the operators depend upon those of the articulation generation function deployed. The necessary and sufficient conditions that must be satisfied by the articulation generating function in order for the algebraic operators to sat- isfy properties like commutativity, associativity and distributivity have been iden- tified in this work. Based on whether these properties are satisfied, a task of com- posing multiple ontologies can be expressed as multiple equivalent algebraic expressions. Using a cost model, the most optimal algebraic expression can be chosen and executed to derive the composed ontology. 5.1 Introduction The semantics of an information source is captured by its ontology, the collec- tion of terms and their relationships as used in the domain of discourse for the source. Most of the focus of ontologists has been on developing ever larger, static ontologies[12], without an explicit contextual constraint, even though the devel- opmental efforts were typically initiated in a specific application domain. When new, related applications arise, existing ontologies must be broadened. For in- stance, to serve a set of intelligence queries hundreds of new definitions had to be added to the already very broad Cyc ontology [14]. We argue below that it is impossible, and not even desirable to achieve a com- prehensive ontology that is also globally consistent. To satisfy the needs of an ap- plication no single source is adequate, and therefore, we have to exploit a universe of sources. These sources are autonomous, and hence, without a global mandate,