Continuous Information Systems

Abstract

In this paper we generalise the notion of ( algebraic ) information system to continuous information system . Just as algebraic information systems are concrete representations of Scott domains, continuous information systems are concrete representations of continuous Scott domains. The class of continuous information systems can be generated from the subclass of qualitative information systems , in the sense that the category of continuous information systems is equivalent to the Karoubi envelope of the category of qualitative information systems. Because qualitative information systems correspond to the qualitative domains of Girard ( Theoret. Comput. Sci. 45, 159-192 (1986)) this implies that the category of continuous Scott domains is equivalent to the Karoubi envelope of the category of qualitative domains. We show how constructions on qualitative information systems (such as product and function space) can be "translated" to constructions on continuous information systems. Among other things, we prove that the category of qualitative information systems is weak Cartesian closed . Finally, we define two universal information systems.