Understanding Partially Ordered Sets: General and Specific Elements Explained

[EvLer]

I came across this sentence in one article and can't make too much sense out of it:
"... the set of points in a partially ordered set can be represented by its most general and its most specific elements".

Any explanation is very much appreciated.

 

[mathwonk]

that is just horse s**t. does that help? i.e. get a better book.

 

[HallsofIvy]

I wouldn't say it quite the way Mathwonk did but I can't make anything out of it either. In particular, the elements of a partially ordered set are not necessarily points!
Is it possible that this is a in a specific application where "general and specific elements" has a given definition?

 

[cronxeh]

You referring to http://acl.ldc.upenn.edu/C/C96/C96-2149.pdf

The Version Space Method
There are a variety of methods in the AI literature
for learning from exarnples. For handling our
task, we have chosen tile so called "version space"
method (also known as the "candidate elimination
algorithm"), cf. (Mitchell, 1982). So we need to
have a look at this method.
Tile basic idea is, that ill all representation languages
for the rule space, there is a partial ordering
of expressions according to their generality.
This fact allows a compact representation of the
set of plausible rules (=hypotheses) in the rule space,
since the set of points in a partially ordered
set can be represented by its most general and its
most specific elements. Tile set of most general
rules is called the G-set, and tile set of most specific
rules tile S-set.

 

[matt grime]

I think it's trying to say something like: to keep track of a partially ordered set that has finitely long chains only, then all we need to do is keep track of the ends of all the chains, ie the maxima and minima.

 

[HallsofIvy]

Ah- thanks to both of you- that is a very specialized vocabulary, then!

 

[MathStudent]

Is that a well known journal or something? How the hell did you (Cronxeh) recognize the original document from a couple of obscure lines. ( yoda? )

 

[Muzza]

Possibly by googling.

 

[CrankFan]

He googled for the phrase that EvLer provided.

 

[MathStudent]

I see...pretty crafty, for a minute there I was thoroughly impressed.

 

[cronxeh]

yes.. impressed you were indeed :rofl:

 

[EvLer]

Didn't realize that meaning was so context-dependent.
Thanks much.