In domain theory, a branch of mathematics and computer science, a Scott information system is a primitive kind of logical deductive system often used as an alternative way of presenting Scott domains.
A Scott information system, A, is an ordered triple
The return value of a partial recursive function, which either returns a natural number or goes into an infinite recursion, can be expressed as a simple Scott information system as follows: That is, the result can either be a natural number, represented by the singleton set
The propositional calculus gives us a very simple Scott information system as follows: Let D be a Scott domain.
Then we may define an information system as follows Let
be the mapping that takes us from a Scott domain, D, to the information system defined above.
denote the set of points of A with the subset ordering.
In general, for any Scott domain D and information system A where the second congruence is given by approximable mappings.