From: pat hayes (phayes@ihmc.us)
Date: 11/18/03
>The OWL-Space (formerly DAML-Space) effort has gone through a long
>period of quiesence, due primarily to a lack of adequate funding here.
>This problem isn't entirely solved, but here at ISI we have money that
>will allow Tom Russ and me to pursue it in a serious way for the next
>few months.
Hey, lucky you.
>That should at least get it well launched.
>
>The first order of business is to bug those people who agreed to (or
>suggested they might) send out a list of their requirements. I won't
>name names, since I've been the most derelict of the bunch. But we
>hope to come up with an initial specification in a week or two of what
>needs to be covered and the more requirements statements we have by
>then the better it will be.
Suggestions (in random order):
1. Ontology should be adequate to represent/describe/interact with
geographical information types conventionally encoded by recognized
cartographic techniques, eg contour/terrain, transportation
connectivity, chloropleth mapping, etc.. It also ought to be able to
handle issues like scale, map resolution, map projections, etc..
2. For the purely topological stuff (boundaries, endpoints,
inside/outside and so on) it ought to be that case that a 1-d slice
through a 2- or 3-d space gives the same kind of topology as a 1-d
topology (eg the Allen interval structure). This can be used as a
reality check on a theory of spatial boundaries.
3. 1-d 'paths' in 2/3-space serve two different purposes: they act as
paths - ways from one place to another - and also as boundary lines.
I suggest that you keep these uses distinct in the ontology: paths
have a direction, boundaries have sides , like a piece of paper. Its
often useful to be able to distinguish the sides, but standard
topology doesn't have any obvious way to do that.
4. Contrary to the above suggestion, much spatial/geographical data
(eg see NIMA data models) is based on a spatial hierarchy built
piecewise from points, where a linesegment is 2 points (the ends), a
line is a series of segments, a closed line is a line with the same
endpoints, a surface-polygon is the region bounded by a closed line,
and a surface is an edgewise-connected set of polygons. (Obvious
connection with techniques of map digitizing by tracing and
clicking.) This is a powerful idea which you might want to retain in
the ontology somehow. Suggestion: treat a place on the surface of the
earth(eg the location of a city) as being a polygonal (2-d) 'box' of
a certain height. This won't work for eg. weather phenomena, but it
might be a good geographical approximation. And then you can always
define the point where a path into a location crosses the boundary as
being either one of the boundary points or else a crossing of two
line segments, one in the path and the other part of the boundary.
5. Boundaries are crucial (for time, boundaries are trivial). Basic
point is that in n-space, boundaries are dimension (n-1), and that
every boundary always has exactly 2 sides almost everywhere ('almost'
because of things like Utah/NewMexico at 4 corners). In n-space,
something of dimension less than (n-1) is never a boundary: so e.g. a
county boundary is either 2-d (now high? - same height as the county,
presumably) or else if its 1-d then a county is 2-d.
6. A while ago we developed a basic geographical/spatial ontology for
NIMA based on 'locations' and 'boundary parts'. Basic relations are
inside (between locations) and at the edge (between location and
boundary part). Boundary parts are themselves locations and can have
boundary parts, etc,. The interesting thing was that in order to make
map semantics work out right, we had to make a basic assumption which
is a kind of geographical comprehension principle: any set of
locations has a unique minimal enclosing location (ie they are all
inside it). Turns out that is a very powerful axiom and you can
derive a lot from it, but as stated its not first-order. So you
probably need to weaken it to some first-order-izable version.
6a. Another thing we found is that boundaries in a digital space (eg
when describing a pixellated screen surface) come in 2 kinds: true
topological boundaries between the pixels (and therefore not part of
the pixel surface!), and visible boundary lines 1 pixel wide used in
graphic applications, and they obey fundamentally different laws, so
its a mistake to try to identify them.
7. Examine the unspoken assumptions of existing spatial ontologies
very carefully. There are a lot of 'mathematically' oriented spatial
ontologies that make basic topological assumptions that don't have
any foundation in geographical intuition, eg that all locations must
be regular sets (Asher&Vieu, ijcai1995). In general, I don't trust
mereology, but I guess that's just my problem.
8. Unlike objects, locations don't have holes. The hole *is* a location.
---
Not all about requirements, I guess. OK, more to the requirements point:
1. Able to interact with basic cartography. For example: same
terrain, different scales/information on two maps is a coherent idea.
2. Needs to be able to deal with the fact that maps represent
information about objects which are too small to be directly
represented at the scale of the map (happens all the time).
3. It should be more motivated by utility than mathematical elegance.
Most general mathematical theories of space are useless in any case,
eg. check out how hard it is to prove the Jordan curve theorem, which
ought to be obvious. Also, lines you can see or draw with a pencil
are not mathematical lines.
4. Any spatial intuition you can illustrate in a digital display
requires axioms which do not assume either mathematical continuity or
discreteness of the underlying space.
>It would also be good to get an updated list of spatial reasoning
>resources that are available at various places, and an updated list of
>similar efforts we should coordinate with.
USGS, NIMA. You can Google several summary lists of existing spatial
ontologies, but see point 7 above.
Pat
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