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.

Definition

A Scott information system, A

satisfying

Examples

Natural numbers

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:

.

.

Propositional calculus

The propositional calculus gives us a very simple Scott information system as follows:

Scott domains

Let D be a Scott domain. Then we may define an information system as follows

• the set of compact elements

be the mapping that takes us from a Scott domain, D, to the information system defined above.

Information systems and Scott domains

, we can build a Scott domain as follows.

is a point if and only if

denote the set of points of A will be a countably based Scott domain when T is countable. In general, for any Scott domain D and information system A

where the second congruence is given by approximable mappings.

See also

• Scott domain

• Domain theory

References

• Glynn Winskel: "The Formal Semantics of Programming Languages: An Introduction", MIT Press, 1993 (chapter 12)