Information systems revisited — the general continuous case

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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.

Keywords

Continuous domains
Information systems

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This work has jointly been supported by the German Research Foundation (DFG) and the National Natural Science Foundation of China (NSFC), respectively, under grants no. 446 CHV 113/240/0-1, 10371106 and 10410638. The work of the first author has moreover been supported by the German Research Foundation (DFG) under grant no. 436 RUS 113/850/0-1(R).