Re: OWL-Space

From: pat hayes (
Date: 11/18/03

  • Next message: Austin Tate: "Re: OWL-Space"
    >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.
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