Supporting Partial and Complete Sets and Tuples in Deductive Databases

In a nested relational database or complex object database, nested tuples and sets are used to represent real world objects. A relation is just a set of tuples and a database is a tuple of relations. For various reasons, a database may contain partial (incomplete) sets and tuples as well as complete sets and tuples in its relations. In this paper, we study how to integrate information about tuples and sets spread in the database and how to check inconsistency in the meantime. Then we define the semantics of a database which allow both partial and complete set and tuples. Finally, we propose a logic-based language that extends Relationlog [2] with null/unknown (⊥) and inconsistent (⊤) values. It supports the null extended nested relational algebra operations as defined in [1] directly and more importantly recursively which makes it more powerful than existing languages. The key feature is the introduction of the two notions into the deductive framework: equivalence (≅) and equality (=) so that for the two special values ⊥ (null/unknown) and ⊤ (inconsistent), we have ⊥ ≅ ⊥, ⊤ ≅ ⊤, but ⊥ ≠ ⊥, ⊤ ≠ ⊤. The intuition for ⊥ (or ⊤) here is that two appearances are equivalent in terms of the information they carry but are not equal as their can be replaced by different values. This work provides a logical foundation for nested relational and complex object databases that have both partial and complete sets and tuples. Especially, it provides a general mechanism to deal with null/unknown and inconsistent values in deductive databases.