A Note on Finitely Derived Information Systems

The notion of information system initially introduced by Scott provides an efficient approach to represent various kinds of domains. In this note, a new type of information systems named finitely derived information systems is introduced. For this notion, the requirement for the consistency predicate used in Scott's information systems is simplified, and the reflexive and transitive rules for the entailment relation are preserved while the finitely derived rule is introduced. A comprehensive investigation is made on the interrelation between finitely derived information systems and algebraic domains. It turns out that their corresponding categories are equivalent, which indicates that the proposed notion of finitely derived information system provides a concrete approach to representing algebraic domains.