work on the ontology of coordinate reference systems

[Chris Partridge]

Hi,

We are now revisiting some work on the ontology of coordinate reference systems - and the notion of a ‘spatial object’ - that we started around 15 or so years ago. Now, as we look a little more closely at the details quite a few questions emerge. I’m wondering whether there are people in the community with views on the topic, would be good to hear any thoughts.  

The work is a little technical, so for those without the technical background I will set it up. There is a LOT of material, so I’m going to start setting things up in this first post to see whether anyone is interested. If they are, I can post more.

Plato and Aristotle have a process that starts with the  "τί ἐστι" (ti esti, "what is it?") question - and it seems a good way in here. Overall, we can frame this as trying to understand: what is a Coordinate Reference System (CRS).

Coordinate points are key components of Coordinate Reference Systems (CRSs). So, let’s start small and ask what a single coordinate point is. It’s always good to start with an example, so let’s use ‘Null Island’ (http://en.wikipedia.org/wiki/Null_Island - “the location at zero degrees latitude and zero degrees longitude (0°N 0°E), i.e., where the prime meridian and the equator intersect.”). Let’s link this to a specific CRS - WGS 84 (G1150 - 7661) (https://epsg.io/7661 - an Ellipsoidal 3D Coordinate system CRS).

We often think of a coordinate point as a fixed point in space. But what is characteristic about this Null Island coordinate point specifically, and coordinate points in general, is that it/they remain at the same place over time (in the sense of the same position in the coordinate system). So, Null Island is in the same place (in this sense) today, tomorrow and next week.  From this perspective, it is time invariant, at every time it is in the same place. All coordinate points (in a CRS) are similarly time invariant - at every time in the same place relative to each other.

If one now takes a four-dimensional spacetime perspective, then the coordinate point places at each time can be taken together and fused into a trajectory over time. In relativity, this is known as a worldline (https://en.wikipedia.org/wiki/World_line - “The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime.”) So Null Island is (from a spacetime perspective) the worldline that is at 0°N 0°E at each point in time.

All the coordinate points in the WGS 84 (G1150 - 7661) CRS are also (from a spacetime perspective) worldlines. And this family of worldlines (belonging to the CRS) do not intersect and cover the relevant portion of spacetime (as every point in the bit of spacetime the coordinate system covers has a (different) coordinate point.) This is a well-known feature in relativity (physics), where it is called a congruence. More specifically, the CRS's set of coordinate point worldlines are called a timelike congruence (https://en.wikipedia.org/wiki/Congruence_(general_relativity)) as the worldlines are (by definition) timelike. (see https://plato.stanford.edu/entries/spacetime-iframes/#InerFramNewtSpac)

In general, a CRS is built using a geodetic datum where a geodetic datum is (according to Wikipedia - https://en.wikipedia.org/wiki/Geodetic_datum) a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates (and related vertical coordinates) or geocentric coordinates. So the datum fixes the coordinate point worldlines and so the timelike congruence.

Specifically, The CRS WGS 84 (G1150 - 7661) is based upon the World Geodetic System 1984 (G1150) datum (https://epsg.io/1154-datum). Other CRSs are based upon this datum - for example: WGS 84 (G1150 - 9055) (https://epsg.io/9055 - an Ellipsoidal 2D Coordinate system CRS); and WGS 84 (G1150 - 7660) (https://epsg.io/7660 - a Cartesian 3D CRS) also use this datum. And so the coordinate points for each of the CRSs pick out the same family of worldlines, the same timelike congruence.

What is also interesting is that the actual coordinates values can differ - the ellipsoidal CRSs are 3D <(0, 0, 0)> and 2D <(0, 0)> - and the Cartesian is <(6378137.000, 0, 0)> - but these all label the same worldline. It is recognised that - and this example shows - that while the timelike congruence is an essential component of the CRS, it is not sufficient to uniquely pick out a particular CRS - see e.g. Nerlich or Norton in these notes (https://en.wikipedia.org/wiki/Frame_of_reference#Notes).

As this also implies, different geodetic datum will differently represent the position of locations on Earth. More specifically, different datums will lead to different Null Islands. So the datum World Geodetic System 1984 (G1674 - 1155)(https://epsg.io/1155-datum) will have a different timelike congruence - and so a different Null Island - 0°N 0°E in its ellipsoidal system - and, in some cases, evolve differently over time (due to, for example, different velocity models. Though these differences may be quite small.

Hopefully you can begin to see now how worldlines and congruences are a natural way to start understanding coordinate systems. Indeed, the above picture can be seen as a physicalization of the topology and geometry that should be familiar from the relativity literature - and its talk of coordinate systems. In this there is much talk of materialising - physicalising the geometry (and topology). There have been a number of ways to describe how this materialises. Einstein talked about a reference mollusc. People also talk about a fleet of clock-carrying particles or perfect fluids or dust or incoherent dust. However, the picture does rely on Einsteinian relativity - it applies equally well to Galilean relativity over Newtonian/Euclidean space-time. It is more about the general structure of spacetime than any specific physical theory (see e.g. Stein, H., 1967, “Newtonian space-time”).

From a more mathematical (topological) perspective, the shift from spacetime to the timelike congruence can be seen as making a quotient space, where the worldlines are the ‘points’ of the new space. If one assumes (as is usually done) the spacetime has a classical mereology. This new space is a ‘spatial’ classical sub-mereology of spacetime. So the standard formalisations of mereotopology (e.g. RCC and Egonhofer) work in this space. This space can be seen as providing a common spatial basis for a set of CRSs - where the mereotopological relations hold across these spaces (and break down when applied to CRSs outside the space, unless they are restricted to a particular specific time).

Something odd appeared in our literature survey though. The relativity literature has extensive discussion of coordinate systems, worldlines and congruences - with links to differential geometry. But the geodesy and geospatial literature has very little - apart from relativistic geodesy, where I guess there is little choice but to engage. Though talk about station positions and velocities gets very close to the notion of congruences. I wonder why this is so. One could hypothesise that as most of the grounding work in geodesy was done in the 18th and 19th centuries, there has been no pressure in the community to take on the ideas in relativity.

Whatever the reason, it seems odd, as the notions of worldlines and congruences seem a natural conceptual framing for coordinate systems. For example, congruences naturally capture the extent of the underlying spatial mereotopology. They also suggest easy ways to formalise using mereotopology. Is there some other underlying reason for this lack of uptake?

[Barry Smith]

you might try asking Alan Ruttenberg -- he has thought about this -- it is truly a gap in BFO support documents, since sites and spatial regions are distinguished, in BFO, by the fact that the latter is determined relative to a frame of reference

did someone give you (4-dimensionists) permission to deal with spatial locations?

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[Ravi Sharma]

Chris

i started reading and saw violations of space and time hence did not go further zero island has to be either between two or more points on earth or inertial if time inveriant

either you are talking of inertial reference or Earth reference

you need to clarify that

for Earth NASA Google and now AI? may help

for inertial we have probes managing beyond solar system and astrophysics almost to end of physical universe

space time comes into picture only shen you consider relativity

another math and geometry reeuire hou to define Euclid Hilbert affine rtc

I know you know some of this a lot as veteran researcher so why ? is there some new?

regards

Thanks.

Ravi

(Dr. Ravi Sharma, Ph.D. USA)

NASA Apollo Achievement Award

​Former Scientific Secretary iSRO HQ

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[Ravi Sharma]

Chris on further reading, I see that you are referring to mereotopology and yes looking at mathematical point and I am studying the Skyrmion type particles related topology 

So can You all and Berry respond to my related Q 

while physics will almost always deal with finites even at infinitesimal scales mathematical point does not have to obey Planck type limts

therefore is there a case for ontology of these two together?

Regards yes you are in depth but why do you need null island in earth geodesy?

Thanks.

Ravi

(Dr. Ravi Sharma, Ph.D. USA)

NASA Apollo Achievement Award

​Former Scientific Secretary iSRO HQ

Ontolog Board of Trustees

Particle and Space Physics

Senior Enterprise Architect

SAE Fuel Cell Standards Member

[Neil McNaughton]

>>In general, a CRS is built using a geodetic datum where a geodetic datum is (according to Wikipedia - https://en.wikipedia.org/wiki/Geodetic_datum) a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates (and related vertical coordinates) or geocentric coordinates.

 

FYI the “datum” business is more complicated than you might imagine. The US National Spatial Reference System is currently being ‘modernized’ as North American Datum (NAD) 83 and vertical datums such as the North American Vertical Datum (NAVD) 88 are to be replaced with new terrestrial reference frames and a novel geopotential datum. The changes are designed to incorporate a ‘dynamic earth’ i.e. with mobile tectonic plates and time-variant datums.

 

Also a good reference for geodesy etc is the European Petroleum Survey Group https://EPSG.org  and its Geodetic Awareness page https://epsg.org/geodetic_awareness.html.

 

My 2 cents… The topic is one for specialists. There is a lot of prior art. Also in my humble opinion, RDF is a poor tool for science and engineering. Modeling with RDF quickly becomes idiosyncratic and unintelligible to the domain specialist. Perhaps this is the intent?

 

I nonetheless very keen to hear of examples of successful RDF modeling in a scientific context.

 

Best regards,

Neil McNaughton

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My 2 cents

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[Chris Partridge]

Hi Barry,

Do we need permission?

It would be good if Alan took a look.

This (as you know from our discussions)  is building upon prior work. 

Chris

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[Chris Partridge]

Hi Ravi,

There is a detailed geodesy aspect to the topic (and a relativity one), that I am hoping doesn't need to be gone into.

While "Skyrmion type particles related topology" and e.g. 'causal set theory' are extremely interesting. I'm working in the space of coordinate systems. And I'm hoping that we can abstract away from these technical matters for this perspective. What would be interesting is if topics such as "Skyrmion type particles related topology" could shed light on this more general topic. Be good if you could point us to something along those lines.

This is more about the 'philosophy' (ontology) of space, time and spacetime - and how it can frame discussions in geodesy and geospatial information.

You asked: ... but why do you need null island in earth geodesy?

I was using this as a starting point for the 'ontological' analysis. I was looking for an interesting coordinate point to discuss - and this is what people often choose.

Geodesy uses coordinate systems - Geodesy defines global and regional reference frames like WGS84. These systems contain points. So I thought it would be easiest to start with the points. These have a much simpler structure than the whole system.

Chris

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[Chris Partridge]

Hi Neil,

let me reply inline ...

Chris

On Fri, 6 Feb 2026 at 08:48, Neil McNaughton <nei...@oilit.com> wrote:

>>In general, a CRS is built using a geodetic datum where a geodetic datum is (according to Wikipedia - https://en.wikipedia.org/wiki/Geodetic_datum) a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates (and related vertical coordinates) or geocentric coordinates.

 

FYI the “datum” business is more complicated than you might imagine. The US National Spatial Reference System is currently being ‘modernized’ as North American Datum (NAD) 83 and vertical datums such as the North American Vertical Datum (NAVD) 88 are to be replaced with new terrestrial reference frames and a novel geopotential datum. The changes are designed to incorporate a ‘dynamic earth’ i.e. with mobile tectonic plates and time-variant datums.

 

Yes, the geodesy quickly gets complicated, so the idea here is to rise above this and look at the general mereotopology and geometry.

 

Also a good reference for geodesy etc is the European Petroleum Survey Group https://EPSG.org  and its Geodetic Awareness page https://epsg.org/geodetic_awareness.html.

The ISO (if you can get hold of them) and OGC standards are useful too. (For transparency, note I am a member of the UK's ISO  IST/36 - Geographic information committee)

 

My 2 cents… The topic is one for specialists. There is a lot of prior art. Also in my humble opinion, RDF is a poor tool for science and engineering. Modeling with RDF quickly becomes idiosyncratic and unintelligible to the domain specialist. Perhaps this is the intent?

Umm, I think there is a topic for our community in how space, time and spacetime work together. As far as I can tell, this is to some extent orthogonal to the geodesy and relativity details.

There is a lot of literature on this topic in various areas, including the philosophy of space and time, which has close links to relativity.

There seems to be a lot less in geodesy and geospatial information.

It is acknowledged as an issue in e.g the ISO standards: the Introduction of ISO 19108:2002 says: “Behaviour in time may be described more easily if the temporal dimension is combined with the spatial dimensions, so that a feature can be represented as a spatiotemporal object. … This International Standard has been prepared in order to standardize the use of time in feature attributes. Although it does not describe feature geometry in terms of a combination of spatial and temporal coordinates, it has been written to establish a basis for doing so in a future standard within the ISO 19100 series.” There is also a link noting Einstein's relative space in the same standard.

If you wish, I can point to other sources that acknowledge this as a known issue.

This is, as I said, an area I have been working on for a while. See, for example, some of my geospatial reference systems papers

• Partridge, C. (2011). An Information Model for Geospatial and Temporal References. https://www.academia.edu/39988229
• Partridge, C. (2013). Geospatial and Temporal Reference – A Case Study Illustrating (Radical) Refactoring. ONTOBRAS-2013 6th Ontology Research Seminar in Brazil. https://www.academia.edu/27433806/
• Partridge, C., Mitchell, A., Loneragan, M., Atkinson, H., de Cesare, S., & Khan, M. (2019). Coordinate Systems: Level Ascending Ontological Options. 2019 ACM/IEEE 22nd International Conference on Model Driven Engineering Languages and Systems Companion (MODELS-C), 78–87. https://www.academia.edu/40354620
• Partridge, C., Mitchell, A., Loneragan, M., Atkinson, H., de Cesare, S., & Khan, M. A. (2020). The Fantastic Combinations and Permutations of Coordinate Systems’ Characterising Options. The Game of Constructional Ontology. https://www.academia.edu/118060077/

 

I nonetheless very keen to hear of examples of successful RDF modeling in a scientific context.

I'm not sure what this has to do with RDF. 

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[Joshua Lieberman]

Hi Chris, et al,

There is active work on a CRS ontology by OGC and W3C groups based on the standards and models from both OGC and ISO TC211. https://github.com/opengeospatial/ontology-crs

There is also an important omission in Chris’ exposition, which is “object”. The geocentric CRS models (and geodetic framework on which they rest, are intended to locate objects on the earth’s (or other planetary bodies’) surface using coordinates. This is an important consideration when thinking about coordinate reference systems because there is nothing static or eternally persistent about the earth’s surface. Geodetic datums are dated not just for historical interest. The high-resolution ones are updated yearly in order to maintain sufficient accuracy with regard to object locations in the face of continental drift and other tectonic forces. Yes, it’s complicated, but for good reason when the real world (or an accurate virtual representation) is involved.

—Josh Lieberman

On Feb 6, 2026, at 4:36 AM, Chris Partridge <partri...@gmail.com> wrote:



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[Sandro Rama Fiorini]

Hello Chris! We published and standardized some work on that topic a long time ago. Our take was much simpler than what you are describing, but it might interest you nonetheless:

- Paper: https://ieeexplore.ieee.org/abstract/document/6696603

- IEEE 1872: https://ieeexplore.ieee.org/document/7084073

best,

Sandro

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[Alex Shkotin]

Chris,

Examining the definitions of various coordinate systems in various sciences and technologies is a large and painstaking undertaking.

I can only share an application of Hilbert's "coordinate system" approach in Foundations of Geometry.

In my own words, but as close to Hilbert's ideas as possible:

A coordinate system in space, for example on a plane, is a figure consisting of two perpendicular lines, on each of which a point distinct from the intersection point (called the origin and usually denoted by O) is chosen and uniquely named. The traditional names for one of the points are X and for the other, Y. The lines on which they are located are called the X- and Y-axes, respectively. The corresponding rays O-X and O-Y are called the regions of positive coordinates, respectively, the X- and Y-axes.

The segments O-X and O-Y are considered unit segments of their axes and are usually equal in length. Any point on the plane is uniquely associated with its X coordinate: a segment or point labeled X. The segment must also have an attribute: a sign with the values "+" or "-" depending on which direction from O it should be placed: "+" toward X, "-" toward the opposite direction. The same applies to Y.

Thus, to present coordinates, one must specify a pair of correctly attributed segments and points somewhere, perhaps on another plane parallel to the given one.

Hilbert's originality lies in the fact that he doesn't operate with non-geometric entities—real numbers.

Which requires a separate transition.

So, for Hilbert, a coordinate system is a labeled figure like this one.

It would be interesting to gather definitions from various theories and technologies in one place. I'd like to participate.

Alex 

чт, 5 февр. 2026 г. в 20:51, Chris Partridge <partri...@gmail.com>:

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[Chris Partridge]

Hi Alex,

In the context of GeoSpatial systems it is an interesting question what a coordinate reference system is.

https://en.wikipedia.org/wiki/Spatial_reference_system --- A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on, or relative to, the surface of Earth as coordinates. It is thus the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space. A particular SRS specification (for example, "Universal Transverse Mercator WGS 84 Zone 16N") comprises a choice of Earth ellipsoid, horizontal datum, map projection (except in the geographic coordinate system), origin point, and unit of measure. Thousands of coordinate systems have been specified for use around the world or in specific regions and for various purposes, necessitating transformations between different SRS.

While making no claims for the accuracy of the Wiki description, it is broadly correct that "It is thus the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space."

As the earlier example of Null Island shows, a coordinate point in a coordinate reference system is something more than one in a Hilbert geometry. (BTW I admire Hilbert's geometry)

One also probably needs both a little more and a little less structure to replicate the multiple timelike congruences that underlie the multiple coordinate reference systems.

Best,

Chris

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[Chris Partridge]

Hi Josh,

Excellent link!! (also click through to https://www.w3.org/groups/wg/sdw/ - Spatio-temporal Data on the Web Working Group) --- Admirable goal: "The ultimate goal is to attain a web ontology for coordinate reference systems (CRS), approved both by the OGC and the W3C."

WRT: "There is also an important omission in Chris’ exposition, which is “object”. The geocentric CRS models (and geodetic framework on which they rest, are intended to locate objects on the earth’s (or other planetary bodies’) surface using coordinates."

Yes, absolutely. This is one of the justification for having coordinate reference systems.

From a methodological perspective. As I said in the original post, for clearing up ontological matters, I am following a plan that starts small and expands out. We have been working on this relation already - and at some stage in the exposition we need to discuss it. So more of a later treat than an omission. 

I see this site ( https://github.com/opengeospatial/ontology-crs) inherits some ISO definitions: 

coordinate system: A coordinate system is a set of mathematical rules for specifying how coordinates are to be assigned to points.

coordinate reference system: A coordinate reference system (CRS) is a coordinate system that is related to an object by a datum.

datum: A datum is a parameter or set of parameters that define the position of the origin, the scale, and the orientation of a coordinate system.

https://isotc211.geolexica.org/concepts/93/ - coordinate system
set of mathematical rules for specifying how coordinates are to be assigned to points
[SOURCE: ISO 19111:2019]

https://isotc211.geolexica.org/concepts/703/ - coordinate reference system
coordinate system that is related to an object by a datum
Note to entry: For geodetic and vertical datums, the object will be the Earth.
[SOURCE: ISO 19111:2019]

I am hoping to get some clarity, as I said at the beginning of my post, on the "τί ἐστι" (ti esti, "what is it?") question applied to points in the definition above.

I have found some definitions that might get us started: 

https://isotc211.geolexica.org/concepts/1166/ - geographic point location
well defined geographic place described by one coordinate tuple
[SOURCE: ISO 19145:2013]

https://isotc211.geolexica.org/concepts/1167/ - geographic point location representation
syntactic description of a geographic point location in a well known format
[SOURCE: ISO 19145:2013]

also ...

https://isotc211.geolexica.org/concepts/347/ - position
data type that describes a point or geometry potentially occupied by an object or person
Note to entry: A direct position is a semantic subtype of position. Direct positions as described can only define a point and therefore not all positions can be represented by a direct position. That is consistent with the "is type of" relation. An 19107 geometry is also a position, just not a direct position.
[SOURCE: ISO 19133:2005]

But, as one digs down, one gets the feeling that some prevarication is going on. Especially if one looks at the relativity literature where things are much much clearer.

@josh - if you have any insight into this or related matters, it would be appreciated.

Also, it seems to me that while there is a lot of complicated technical matter here, the relation between space and time is relatively (excuse the pun) straightforward if you bite the bullet and try to make things clear. It is a conceptually cleaner and simpler part of the overall system.

Best,

Chris

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[Ravi Sharma]

Chris

Many thanks for details and references. I went to your most recent reference in your reply in this thread.

It opens my eyes on at least more than 2 or 3 decades of work you have been doing on Business Objects ontology and standards and related research.

I plan to soon revert to see if I can relate to your Null Ontology and your Q. I also plan to sound out particle topologists.

I can see applications already to constellations of multiple LEO and MEO objects and also viewing opportunities from those of a fixed space-time object such as a point tied to time and space on Earth or in these orbits.

As a physicist, not beyond a student, my understanding is that multiple tuples and multipole expansions of basic geoids, replaced by numeric realtime gravitational (geodetic) points on and near earth space depend on realtime values of mundane things like rain and cloudmass movements as well as known anomalies such as Bermuda Triangle related to mass anomalies in earth crust or surface.

Why would these be related or helped by your Null Island abstraction for Earth Geodesy?

I am excluding Math and metaphysical Ontology for the time being not having studied those.

Appreciate your extensive work.

Regards.

Thanks.

Ravi

(Dr. Ravi Sharma, Ph.D. USA)

NASA Apollo Achievement Award

Former Scientific Secretary iSRO HQ

Ontolog Board of Trustees

Particle and Space Physics

Senior Enterprise Architect

SAE Fuel Cell Standards Member

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[Alex Shkotin]

Chris,

The mathematics and physics of WGS 84 are very interesting. I'll have to look into it. I'd start with the South Pole—it's the only place where one of the axes meets solid ground, albeit icy, and it moves 10 meters per year. But they say that even if there were rock at the point where the axis meets solid ground, it would still move. What progress has mathematical usage made!

I would ground mathematical models of spacetime in the corrections of general relativity and special relativity for satellite navigation. But I'm a long way from that.

Best,

Alex

пт, 6 февр. 2026 г. в 20:03, Chris Partridge <partri...@gmail.com>:

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[Mike Peters]

Chris,

This is a great project. I need to use 4D Spacetime in Pipi 10 (the next version). I will read all this with great interest.

I have used a great deal of your and Matthew West's previous work. All excellent. Thank you.

Mike Peters

NZ
https://www.blog.ajabbi.com

[Chris Partridge]

Hi Mike,

Good to hear from you.

Be really useful to hear any experiences you have with geospatial systems in Pipi 9 and 10.

Chris

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[Chris Partridge]

Hi Ravi,

Be really useful if you could find some connections with the more technical areas in physics.

The target is the standard geospatial structures used in the ESPG and PROJ databases (https://proj.org/en/9.3/index.html), but we have found that when building the mereotopology (and geometry) for these that some of the more technical work provides useful scaffolding.

For example, when trying to formalise what a worldline is, the work on causal structures (https://en.wikipedia.org/wiki/Causal_structure) in Lorentzian manifolds by Penrose, Hawking et al gives a useful framework that we can reuse.

Within our scope of "the standard geospatial structures used in the ESPG and PROJ databases" we consume the work done on "mass anomalies on the earth's crust or surface" to fix the coordinate systems, but these are (it seems to me) mostly out of core scope.

Chris

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[Chris Partridge]

Hi Barry,

WRT: "since sites and spatial regions are distinguished, in BFO, by the fact that the latter is determined relative to a frame of reference"

A quick search threw up the superseded document: http://ontology.buffalo.edu/bfo/Reference/old%20versions/BFO_Nov9_noon.pdf

Which says: 

2.1.2.3 Spatial region

We recommend that users of BFO:spatial region specify the coordinate frame which they are

employing, for example, when dealing with spatial regions on the surface of the Earth, the coordinate

frame of latitude and longitude. Such coordinate frames can be associated with a Newtonian or a

relativistic frame of reference. The reference frame might be relative to a moving object such as the

earth, in which case the corresponding spatial regions move with the movement of the earth.

However, they are at rest relative to their coordinate frame. Lines of latitude and longitude are two dimensional object boundaries which can move; however, they are by definition at rest relative to the

coordinate frame which they determine.

Elucidation: A spatial region is, intuitively, a 0-, 1-, 2- or 3-dimensional part of space. This

elucidation will fall short, however, unless it is understood in a way that conforms with what we

know from the theory of relativity. One step in this direction is to add: a spatial region is the sort of

entity that can be specified by means of a coordinate frame, and is always at rest relative to this

coordinate frame.

Example: The Tropic of Capricorn (with the coordinate frame defined by the lines of latitude and

longitude)

Spatial regions have no qualities except shape, size and relative location.

Object boundaries and sites are distinguished from the spatial region which they occupy at any given

time in the sense that (1) the former move when their material host moves, and they change shape or size when their material host changes shape or size; (2) the latter must be specifiable in terms of some system of coordinates, and they are by definition at rest relative to this coordinate frame.

I'm guessing that this is still a reasonably accurate statement of the position.

Chris

On Thu, 5 Feb 2026 at 19:02, Barry Smith <ifo...@gmail.com> wrote:

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[Chris Partridge]

Hi Sandro,

I noticed this in your paper.

"Such as with time in SUMO, we introduce the notions of position point and position region. A position point refers to a point in a coordinate system projected on the physical space. A position region is an abstract region in a coordinate system overlapping the physical spatial region occupied by the object. Both position point and position region are types of position measurement; i.e., ∀p PMeasure(q) ↔ PPoint(q) ∨ PRegion(q) and ∀q PPoint(q) → ¬PRegion(q). 

Also, it is important to note that all these definitions are synchronic; i.e., they consider only situations like snapshots in time. As such, two objects cannot have the exact same quantitative position; i.e., they can not be located at the same position point.   

Operationally, it is quite clear how this works. The interesting question is what the position point and position region are.

On a first reading, it seems they persist in time as they are used at various different snapshots in time.

My analysis so far would see position points as (4D) wordlines and position regions as (4D) worldtubes. 

This interpretation seems to be consistent with both usage and intention - and give a simple physical (mereological) meaning to the PMeasure predicate. 

Does this work for your intuitions?

Best

Chris

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[Sandro Rama Fiorini]

Hello, Chris.

>  On a first reading, it seems they persist in time as they are used at various different snapshots in time.

Yes, if memory serves me right. Time was not one of our main concerns, so we did not include it explicitely.  

Maybe one could try to achieve some sort of diachronic use of the ontology by means of SUMO's modal axioms (e.g., holdsDuring).

> My analysis so far would see position points as (4D) wordlines and position regions as (4D) worldtubes. 

> This interpretation seems to be consistent with both usage and intention - and give a simple physical (mereological) meaning to the PMeasure predicate. 

> Does this work for your intuitions?

It makes sense to me. At the very end of the conclusion we mentioned something like that as a possible extension, so probably some of us were already thinking in that direction. 

However, what you are doing seems much more sophisticated, especially if you take relativity into account. I am not sure that we could make POS compatible with relativity, even though we did not assume a universal reference frame,

best,

Sandro

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[Chris Partridge]

Hi,

WRT: Maybe one could try to achieve some sort of diachronic use of the ontology by means of SUMO's modal axioms (e.g., holdsDuring).

Exactly. This is the nub of the challenge. Working out the nature of and the tradeoffs on the holdsDuring for the general case. You can see these in action when you look at the spatial embedding of coordinate reference systems. Of course, you can simplify things for local cases.

Chris

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[Mike Peters]

Hi Chris

I have been thinking about how to proceed. These are some initial ideas specific to Pipi 9 and 10.

A couple of years ago, when Matthew was still alive, I did a deep dive into your book, talks and papers, and all those of Matthew I could find. Especially BORO, NATO, Shell Oil Refineries, and the UK Digital Twin Project for Built Infrastructure.

All outstanding work in my opinion.

As a result, I was convinced of SpaceTime, not Space and Time. The advances in Science support this.

• https://www.blog.ajabbi.com/2023/08/matthew-west-1953-2023.html

As previously discussed on this forum, I reverse-engineered the material above and built my own Boro Engine (bor) for Pipi 9. It's not in production yet, but it works and can go forward and backwards. It uses 4D'ism SpaceTime in the underlying data model.

• https://www.blog.ajabbi.com/2024/12/dafni-conference-2024.html

There are a number of different spatial situations that require different kinds of optimised servers.

• The Universe (satellite navigation)
• Earth as a geography (GIS server)
• Inside buildings (CAD maybe??)
• etc

• https://www.blog.ajabbi.com/2025/11/workspaces-for-built-environment.html

The question now is how to make that work with a GIS Server for the world driven by a GeoDatabase using GeoServer and PostGIS+PostgreSQL.

• https://www.blog.ajabbi.com/2026/02/gis-mapping-options.html

Years ago, when NZERN received the ESRI Conservation Grant with all that GIS Software, I created geodatabases with a time column in every table to track changes.

• A forest might grow in extent over time
• A lake's composition might change over time without changing its extent.

I also hacked ESRI JTX as a way to store changes over time. (not what it was designed for)

Future work on Pipi 10 (2027)

I don't think GeoServer 3 has that spacetime functionality built in. But spacetime could be incorporated into GIS via the Geodatabase. I thought an SQL link between the Boro Engine (bor) database and the GIS Geodatabase might work.

I need to do some experiments

Will keep you posted

Mike Peters
NZ
https://www.blog.ajabbi.com

======================

Hi Mike,

Good to hear from you.

Be really useful to hear any experiences you have with geospatial systems in Pipi 9 and 10.

Chris

=================

Chris,
This is a great project. I need to use 4D Spacetime in Pipi 10 (the next version). I will read all this with great interest.

I have used a great deal of your and Matthew West's previous work. All excellent. Thank you.

Mike Peters
NZ
https://www.blog.ajabbi.com