# Ranges

From: David Leal <david.leal@caesarsystems.co.uk>
Date: Thu, 10 Jul 2008 11:16:07 +0100
Message-Id: <1.5.4.32.20080710101607.00cf3f44@pop3.demon.co.uk>

```
Dear All,

Henson's e-mail raised the question of ranges, which are very important for
engineering.

Work on an ontology for geometry came up with the following taxonomy:
Manifold: set of things that is a manifold (see maths textbooks for a
definition)
Manifold1d: Manifold that is 1D (see maths textbooks for the definition of
dimension for a manifold)
ManifoldEdge: Manifold1d that has two boundaries (i.e. ends)
OrderedSet: set of things with an order
DirectedManifoldEdge: intersection of ManifoldEdge and OrderedSet

These concepts are used again and again. Some examples are:

1) Mass - a Manifold1D and an OrderedSet

Mass_range_from_10_to_11kg - a DirectedManifoldEdge, with masses 10kg and
11kg at the ends.

2) Reals - a Manifold1D and an OrderedSet

Real_interval_10_to_11 - a DirectedManifoldEdge, with real numbers 10 and
11 at the ends.

3) Time(TAI) - a Manifold1D and an OrderedSet

Time(TAI)_from_2008-07-010T10:00_to_2008-07-010T11:00 - a
DirectedManifoldEdge with times 2008-07-010T10:00 and 2008-07-010T11:00 at
the ends.

4) Points_in_the_path_of_MyShip_from Busan_to_Shanghai - a Manifold1D and an
OrderedSet

Path_of_MyShip_on_2008-07-12 - a DirectedManifoldEdge with points
latitude-longitude (83.10, 51.23) and (85.32, 53,67) at the ends.

A small topology ontology with the taxonomy above, and the properties:
end1: DirectedManifoldEdge -> Thing
end2: DirectedManifoldEdge -> Thing
would solve all these problems.

Hence we could have:

<topology:end1 rdf:resource="#10kg"/>
<topology:end2 rdf:resource="#11kg"/>
</topology:DirectedManifoldEdge>

Best regards,
David

p.s. Its all simple as I have presented it, but Manifold etc. are all
subclasses of Class. It takes us into the issue of metasubclassing raised by

============================================================
David Leal
CAESAR Systems Limited
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Received on Thursday, 10 July 2008 10:16:41 GMT

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