Difference between revisions of "Ordered relation"
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An [[ordered relation]], or a [[directed relation]] | An [[ordered relation]], or a [[directed relation]] is the generic building block of [[Partially ordered set]]s<ref name=Outline>{{:Paper/Outline of a Mathematical Theory of Computation}}</ref>. It can be visualized as an [[arrow]] that relates two [[object]]s with an explicit direction. The directionality of a [[directed relation]] breaks the symmetry of symbolic representation, which is the smallest amount of information, therefore, [[directed relation]]s can be used to represent any other kinds of information content<ref extends=Outline>Section 2. Data Types and Mappings, Page 6, Axiom 1:A data type is a partially ordered set.</ref>. Ordered relations are particularly useful in representing [[causal relation]]s<ref>{{:Book/The Book of Why}}</ref>. | ||
=Prefix and Postfix Expressions= | |||
Since order matters, the sequence of how certain symbols appears in an expression also matters a lot. There are two kinds of expressions: | |||
# [[Prefix Expression]] | |||
# [[Postfix Expression]] | |||
<noinclude> | <noinclude> | ||
{{PagePostfix | |||
|category_csd=Arrow,Order,Relation,Function,Structuralism,Universal Component,Commutator | |||
}} | |||
</noinclude> | </noinclude> | ||
Latest revision as of 12:41, 17 July 2022
An ordered relation, or a directed relation is the generic building block of Partially ordered sets[1]. It can be visualized as an arrow that relates two objects with an explicit direction. The directionality of a directed relation breaks the symmetry of symbolic representation, which is the smallest amount of information, therefore, directed relations can be used to represent any other kinds of information contentCite error: Invalid <ref> tag; invalid names, e.g. too many. Ordered relations are particularly useful in representing causal relations[2].
Prefix and Postfix Expressions
Since order matters, the sequence of how certain symbols appears in an expression also matters a lot. There are two kinds of expressions:
References
- ↑ Scott, Dana (January 1, 1970). "Outline of a Mathematical Theory of Computation". local page: Oxford University Computing Laboratory Programming Research Group.
- ↑ Pearl, Judea (2018). The Book of Why: The New Science of Cause and Effect. local page: Basic Books. ISBN 978-0-465-09761-6.
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