Abstract Database Category Based on Relational-query Observations

摘要

In this paper we develop a general framework for the Categorical Denotational Semantics of database integration based on views (relational database queries). We define a database category DB different from a Set category, with objects database-instances and with partial-tree morphisms between them: it is used as a semantic domain for a database mappings, based on a set of complex query computations. The graph-schema mappings between databases, based on the first-order logic formulae, constitute the formal ontology of this data integration system and can be functorially translated into this lower-level "computation-based" category DB: intuitively, this translation is a denotational semantics for a formal logic database integration ontology. We assume a new behavioral point of view which produces a lattice ordering and a duality (categorial symmetry) between objects and arrows in the DB category. The introduced observations, which are the query-computations without the side-effects (are not materialized as databases), define a fundamental (from Universal algebra) monad endofunctor T, which is a closure operator for objects and for morphisms also. This denotational semantics is used for the Fixpoint semantics for a query answering in Data Integration Systems [1].