This paper surveys a variety of deductive database theories. Such theories differ from one another in the set of axioms and metarules that they allow and use. The following theories are discussed: relational, Horn, and stratified in the text; protected, disjunctive, typed, extended Horn, and normal in the appendix. Connections with programming in terms of the declarative, fixpoint, and procedural semantics are explained. Negation is treated in several different ways: closed world, completed database, and negation as failure. For each theory examples are given and implementation issues are considered.

The execution model of Prolog, the first popular language based on Horn Clauses, was designed for efficient evaluation on von Neumann architectures. An alternative process model of execution, better suited for parallel evaluation and reactive programming, has given rise to a new class of languages based on Horn Clause logic, concurrent logic languages. There appears to be a profusion of languages which claim to fall into this class and it is difficult for an initiate to appreciate why each is the way it is. One notable member of this class, FGHC, forms the cornerstone of the Japanese 5th Generation Initiative. Fortunately, the seemingly exponential growth in these languages is only an illusion. A finite number of synchronization mechanisms arise from attempting (or sometimes not attempting) to control two principle synchronization difficulties: the premature binding problem and the binding conflict problem. Suitable combinations of these synchronization mechanisms reproduce the languages of this family. A background knowledge of Prolog is assumed and some familiarity with the difficulties encountered in concurrency would be advantageous.