- Scott information system
In
domain theory , a branch ofmathematics andcomputer science , a Scott information system is a primitive kind of logicaldeductive system often used as an alternative way of presentingScott domain s.Definition
A Scott information system, "A", is an ordered triple
*
*
* satisfying
#
#
#
#
#Here means
Examples
Propositional calculus
The
propositional calculus gives us a very simple Scott information system as follows:*
*
*cott domains
Let "D" be a
Scott domain . Then we may define an information system as follows* the set of
compact element s of D
*
*Let be the mapping that takes us from a Scott domain, "D", to the information system defined above.
Information systems and Scott domains
Given an information system, , we can build a
Scott domain as follows.* Definition: is a point iff
**
**Let denote the set of points of A with the subset ordering. will be a countable Scott domain when T is countable. In general, for any Scott domain D and information system A
*
* where the second congruence is given byapproximable mapping s.ee also
*
Scott domain
*Domain theory
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