The theory of deductive database systems

Highlights in three areas are discussed: (1) efficient algorithms for evaluating declarative logic, with ´declarative´ referring to logical rules (if . . . then statements) whose intended meaning is the minimal fixpoint, that is, the set of deducible facts; (2) methods for dealing with nonmonotonic logic, that is, with sets of rules that do not have a unique minimal fixpoint to serve as the natural meaning of the logical rules; and (3) extensions to traditional first-order logic that offer capabilities beyond that found in first-order-logic systems, of which the Structured Query Language (SQL) is the most significant example. These extensions include the ability to support objects, side effects, and higher order features, such as predicates (essentially relation names) as variables. Effectively, these extensions introduce many of the features associated with object-oriented database systems into the domain of logic languages.<>