Unifying spatial entities

[Bjoern Peters]

This is a summary of my argument from the 'Buffalo' email thread. To reduce confusion, I will now label 'spatial entity' what I called 'site' in the previous thread (I did point out that I did not meant bfo:site, but it is buried too many emails down). Lot's of feedback is incorporated - I don't claim that this is original.

'spatial entity' is intended to replace the use of bfo:site, bfo:spatial region and bfo:spatiotemporal region.

'spatial entity' is a primitive, but roughly: A continuant consisting of a spatial shape in relation to some arrangement of other continuants.

A spatial entity has only spatial entities as its parts. Specifically, there are no material entities that are part_of a spatial entity. Rather there is a projection relation 'exactly_located_in' which connects every material entity with exactly 1 spatial entity.

In contrast to bfo:spatial region, spatial entities are defined relative to other entities (no absolute space). In contrast to bfo:site, there are no material parts to a spatial entity.

Movement of material entities is defined as the change of location of a material entity in a spatial entity. This is important, because movements are inherently relative. Driving a car, my location in the interior of the car (a spatial region relative to the car) moves differently from my location on the road (a different spatial region relative to the earth surface). Similarly, there is movement of one spatial region relative to another.

More relations can be defined based on the above. For example, the relation 'contained in' holds between a material entity x and a spatial entity y if the material entity x is located in a spatial entity that is part_of y. Similarly the relation 'overlaps' between spatial entity A and spatial entity B holds if there is a spatial entity C that is part_of spatial entity A and spatial entity B. etc.

Two spatial entity r1, r2 are identical if r1 part_of r2 and r2 part_of r1 for all times t.

Spatial entities can bear qualities such as volume, length, shape.

There are children of spatial entity:
zero-dimensional spatial entity: a spatial entity that has no extension quality. Example: The tip of the needle. An intersection of two one-dimensional sites. The center of mass of a material entity.
one-dimensional spatial entity: a spatial entity that has a length extension quality.
two-dimensional spatial entity: a spatial entity that has an area extension quality.
three-dimensional spatial entity: a spatial entity that has a volume extension quality.

spatial entity can only be part_of other spatial entities of equal or higher dimension

The gut example:
There is an instance of a spatial entity 'lumen of Phil's gut' which is bounded by the gut wall.
There is a collection of material entities (which is a material entity itself) 'content of lumen of Phil's gut', which is is made up of all material entities that are contained in the lumen of Phil's gut.

The bottle containing water and a coin example:
There are instances of material entities, glass bottle, portion of water, coin. Each is located in exactly one site, none of which overlap. The 'fillable volume of the bottle' is a spatial entity bounded by the interior bottle walls and a fiat boundary at the top of the bottle. The coin and the water are both contained in the fillable interior of the bottle.

I will stop here. I hope this is easier to digest than the email thread. I would specifically like to hear if there are things we cannot say with this formalization and that lead us to require the trinity of bfo:site, bfo:spatial region, and bfo: temporal region.

- Bjoern

--
Bjoern Peters
Assistant Member
La Jolla Institute for Allergy and Immunology
9420 Athena Circle
La Jolla, CA 92037, USA
Tel: 858/752-6914
Fax: 858/752-6987
http://www.liai.org/pages/faculty-peters