On Algebraic Query Processing in Logical Databases

Abstract

In this chapter we combine the advantages of two possible logical interpretations of databases — the so-called proof theoretic and model theoretic approaches. These advantages are: computability of the answer for queries by means of relational algebra in the model theoretic approach and generality of the proof theoretic approach. We claim that although database systems should be supplied with inference rules for automatic reasoning, the core of the query answering process should be algebraic, if possible, in the relational algebra-like style.

Certainly any proposed algebraic system for computing answers to queries must be proved correct with respect to the underlying first order theory (i.e., by using algebraic tools we obtain only valid and all valid conclusions which could be derived). Such a correctness criterion is proposed and applied in this chapter.

A new general notion of an answer to a query is defined, and two types of tables (extended relations), previously introduced in order to represent incomplete information are examined from the point of view of their application for algebratization of the query answering process. We show also how techniques introduced here could be useful in approximating answers to queries leading to a two-phase technique incorporating both algebraic and theorem-proving methods.