Question on BFO 2.0 Relations having Time Components

[ANTHONY PETOSA]

BFO Discussion List:

As an example, the "continuant_part_of" relation in BFO 2.0 (draft
documentation) is elucidated as follows:

******************************
'b' continuant_part_of 'c' at 't' =
Def. 'b' is a part of 'c' at 't' & 't' is a temporal region & 'b' and
'c' are continuants.

Domain: continuant
Range: continuant

The range for 't' (as in all cases throughout this document unless
otherwise specified) is temporal region.

******************************

What precisely does the following mean?

1. 't' is a temporal region
2. The range for 't' is temporal region


Elsewhere in the BFO 2.0 documentation (Section 3.15 Temporal Region),
'time(sub R)', where 'R' is a temporal frame of reference, is described
as the "maximal INSTANCE of the universal temporal region." Where "'t'
is a temporal region", does this then mean that some INSTANCE 't' is an
occurent_part_of the maximal INSTANCE 'time(sub R)'? If so, then is "'t'
is a temporal region" another way of saying "'t' instantiates temporal
region"?

Assuming 't' is an instance_of temporal region, how does one explain
"range for 't' is a temporal region"? Is "range" used here in the
conventional English usage, or does range suggest the "co-domain" in a
mathematical mapping? If it is the former, then I view this statement as
there existing one or more 't' instances that reside in an
occurrent_part_of temporal region relative to some reference frame. If
it is the latter, then this suggests that 't' is a relation having
temporal region as its range and (implicitly) BFO Entity as its domain.
Mathematically, this would place "2" ('t' as an edge) in contradiction
with "1" ('t' as a vertex).

Your feedback is greatly appreciated.


Regards,

Anthony Petosa

[Alan Ruttenberg]

On Fri, Apr 12, 2013 at 12:38 PM, ANTHONY PETOSA <ape...@optonline.net> wrote:

BFO Discussion List:

As an example, the "continuant_part_of" relation in BFO 2.0 (draft documentation) is elucidated as follows:

******************************
'b' continuant_part_of 'c' at 't' =
Def. 'b' is a part of 'c' at 't' & 't' is a temporal region & 'b' and 'c' are continuants.

Domain: continuant
Range: continuant

The range for 't' (as in all cases throughout this document unless otherwise specified) is temporal region.

******************************

What precisely does the following mean?

It might be clearer to write a map continuant_part_of c1 -> (c2,t) 

 

1. 't' is a temporal region

Yes 

2. The range for 't' is temporal region

No. 

Elsewhere in the BFO 2.0 documentation (Section 3.15 Temporal Region), 'time(sub R)', where 'R' is a temporal frame of reference, is described as the "maximal INSTANCE of the universal temporal region." Where "'t' is a temporal region", does this then mean that some INSTANCE 't' is an occurent_part_of the maximal INSTANCE 'time(sub R)'? If so, then is "'t' is a temporal region" another way of saying "'t' instantiates temporal region"?

There are two things here.

1) something being a temporal region - in other words being an instance of the universal 'temporal region'

2) That there is a maximal instance of the universal 'temporal region'. Given how the maximum is defined, this means that every instance of 'temporal region' is part of this instance. 

The description as part of is a kind of dual to the description as instance of. As an other example, consider aggregates gold atoms. You can define a class 'any aggregate of gold atom' (GA). You can define an instance of that class which is all the gold atoms in the universe ga(r). Now any particular aggregate of gold ga is both an instance of GA and a part of ga(r). 

 

Assuming 't' is an instance_of temporal region, how does one explain "range for 't' is a temporal region"? Is "range" used here in the conventional English usage, or does range suggest the "co-domain" in a mathematical mapping?

I don't know what the conventional usage is anymore :)

I don't remember what co-domain in mathematical mapping is. Googling...

Yes, it suggests co-domain, but remember that continuant_part_of at t isn't a function.

 

If it is the former, then I view this statement as there existing one or more 't' instances that reside in an occurrent_part_of temporal region relative to some reference frame.

Yes. Once instance is sufficient (and all that is intended) as we make no constraint that t, when a region, is contiguous. Arguably we need to look more closely at this.

 

If it is the latter, then this suggests that 't' is a relation having temporal region as its range and (implicitly) BFO Entity as its domain. Mathematically, this would place "2" ('t' as an edge) in contradiction with "1" ('t' as a vertex).

No. 

Your feedback is greatly appreciated.

As is yours.

 

Regards,

Anthony Petosa

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[Patrick Lapointe]

Hi Anthony,

I am by no means an expert, so dwell on this with reserve,but my understanding about the expression "at t" in BFO relation definitions is that t is a commodity of axiomatic definitions, a time-index component,not a Universal per se.

If it were an Universal at all, it would fit span:Temporal Instant under span:TemporalRegion | span:ConnectedTemporalRegion.

t has Domain Temporal Instant

and Range Temporal Region