Information systems revisited — the general continuous case

Abstract

In this paper a new notion of continuous information system is introduced. It is shown that the information systems of this kind generate exactly the continuous domains. The new information systems are of the same logic-oriented style as the information systems first introduced by Scott in 1982: they consist of a set of tokens, a consistency predicate and an entailment relation satisfying a set of natural axioms. It is shown that continuous information systems are closely related to abstract bases. Indeed, both categories are equivalent. Since it is known that the categories of abstract bases and/or continuous domains are equivalent, it follows that the category of continuous information systems is also equivalent to that of continuous domains. In applications, mostly subclasses of continuous domains are considered. For example, the domains have to be pointed, algebraic, bounded-complete or FS. Conditions are presented that, when fulfilled by a continuous information system, force the generated domain to belong to the required subclass. In most cases the requirements are not only sufficient but also necessary.