Information Algebras and Information Systems

We present a general theory of information processing in computer science. The basic structures considered are those of information algebras. These structures satisfy some intuitive axioms about two fundamental operations on bodies of information, combination of information and focusing of information to a frame. We show that finitary information algebras correspond to a version of Scott’s information systems, provided that the entailment relation satisfies the interpolation and the deduction property. Examples of information algebras are constraint systems, Bergstra’s module algebra and relational databases. We show that every information algebra can be embedded into an information algebra generated by an abstract tuple system.