Temporal association algebra: A mathematical foundation for processing object-oriented temporal databases

This paper describes an object-oriented temporal association algebra (called TA-algebra) which is intended to serve as a formal foundation for supporting a pattern-based query specification and processing paradigm. Different from the traditional table-and-attribute-based paradigm, the pattern-based paradigm views the intension of an object-oriented temporal database as a network of object classes interconnected by different association types and its extension as a network of associated temporal object instances. Consistent with this view, queries can be specified in terms of patterns of temporal object associations or nonassociations (i.e., linear, tree and network structures of object classes/objects with logical AND and OR branches). TA-algebra provides a set of algebraic operators for processing these patterns and allows the direct and/or indirect associations and/or nonassociations among temporal object instances to be more explicitly represented and maintained during processing than the traditional tabular representation of temporary or final query results. TA-algebra operators are based on time-interval and valid-time semantics and they preserve the closure property. The algebra is capable of operating on heterogeneous as well as homogeneous patterns of object associations. Both homogeneous and heterogeneous patterns are decomposed into a set of primitive temporal pattern instances for uniform treatment. This paper formally defines the TA-algebra operators and their mathematical properties. The applications of these operators in query decomposition and processing are illustrated by examples.