Information systems revisited - the general continuous case

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. own that continuous information systems are closely related to abstract bases. 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. The domains have e.g. to be pointed, algebraic, bounded-complete or FS. Conditions are presented that when fulfilled by an continuous information system force the generated domain to belon...

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Dieter Spreen, Luoshan Xu, Xuxin Mao
• Keywords: Continuous Domains, Continuous Information, Information System, TCS 2008, Theoretical Computer Science