This paper looks at the relationship between classical logic and practical systems, which employ logic-based techniques to process data. The emphasis is on answer set programming (ASP) and Datalog rather than Prolog. While Prolog can be considered a full programming language loosely based on classical logic, ASP and Datalog are more limited; however, that enables them to be more closely related to classical logic. An important difference between classical logic and most logic programming is the technique of taking a fact to be false if it cannot be proved true, leading to non-monotonic reasoning, as the addition of a further fact to the data could cause something that was reasoned to be true to no longer be reasoned true.

The paper considers various restrictions on logic rules in order to be able to give a clear formal semantics. The key technique used is that of evaluation stages, starting off with directly defined facts, and then at each stage adding new facts that can be gained directly by applying a rule. A logic program is bounded if this reaches a stage where no more facts will be added. The paper uses this to show that various forms of restrictions are formally equivalent.