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Apr 7, 2021, 4:39:59 PMApr 7

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I wasn't able to find any explicit mention in the literature about whether BFO assumes time to be linear (i.e., totally ordered) or branching (i.e., partially ordered). However, I did notice in "An Axiomatisation of Basic Formal Ontology with Projection Functions" (https://philarchive.org/archive/TREAAO) that the temporal ordering relation is defined as being irreflexive, transitive, and asymmetric, which I believe implies a strict partial ordering. That paper is over a decade old, though, and it doesn't look like an equivalent relation exists in RO temporal-relations.

Apr 7, 2021, 7:33:31 PMApr 7

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Hi,

Snap Span paper made that assumption
"Our apparatus will require a theory of temporal order reflecting the structure
of time as a linear continuum. We follow traditional usage and take as our
primitive the relation Before, a strict total order which holds between two time
instants when the first is earlier than the second." p.154 http://ontology.buffalo.edu/smith//articles/SNAP_SPAN.pdf

As I understand, this has not been revisited in BFO 2.0 and I am not aware of a discussion within the doc (this may have been left undiscussed on purpose). The CLIF proposal seems to take a different approach, based on intervals, but, as I understand, it does not weight on the ordering take. Others will correct me if I'm wrong.

Best,

Pierre

On Wed, Apr 7, 2021 at 9:40 PM Matt Diller <dille...@gmail.com> wrote:

I wasn't able to find any explicit mention in the literature about whether BFO assumes time to be linear (i.e., totally ordered) or branching (i.e., partially ordered). However, I did notice in "An Axiomatisation of Basic Formal Ontology with Projection Functions" (https://philarchive.org/archive/TREAAO) that the temporal ordering relation is defined as being irreflexive, transitive, and asymmetric, which I believe implies a strict partial ordering. That paper is over a decade old, though, and it doesn't look like an equivalent relation exists in RO temporal-relations.

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Apr 7, 2021, 9:52:20 PMApr 7

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BFO-2020 has temporal region, 0d and 1d temporal regions, temporal instants, and temporal intervals. 0d temporal regions are sums of instants. 1d temporal regions are sums of intervals and instants, with at least one interval. The instances are in a total order. The others are partially ordered. The before relation is called precedes.

All temporal regions have a first and last instant. The first and last instances can be asserted part of the interval or not. In the case of intervals, any instant between them is part of the interval. The Allen interval algebra can be defined on top of this but only establishes relations between intervals. I've written those definitions and tested them but they haven't been released as yet.

The temporal theory in BFO-2020 has finite models. We do not have a density axiom or unboundedness axioms. In part this is done in order to make it possible to build a satisfiable finite model in BFO. We in fact do this and that serves as proof the theory is consistent.

Alan

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Apr 8, 2021, 11:57:25 AMApr 8

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Greetings.

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> BFO-2020 has temporal region, 0d and 1d temporal regions, temporal instants, and temporal intervals.

‘Temporal Instant’ and ‘Temporal Interval’ must be addressed formally before tackling temporal ordering in BFO. The draft BFO-2020 documentation does not define “temporal instant”. Also, it contains no formal definition of “temporal interval” but does provide the following informal definition:

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“A temporal interval is a special kind of one-dimensional temporal region, namely one that is self-connected (is without gaps or breaks).”

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BFO-2020 offers the following elucidations:

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A.1.2.75 zero-dimensional temporal region

Elucidation: A zero-dimensional temporal region is a temporal region that is a whole consisting of one or more separated temporal instants as parts.

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A.1.2.76 one-dimensional temporal region

Elucidation: A one-dimensional temporal region is a temporal region is (sic) a whole that has a temporal interval and zero or more temporal intervals and temporal instants as parts.

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I made some observations under separate cover, which I will summarize here.

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- The terms ‘temporal instant’ and ‘temporal interval’ are mentioned throughout the (DRAFT) BFO-2020 documentation, and as already noted, the latter universal is informally defined. However, they are presented as universals with formal definitions.
- The preceding A.1.2.75/76 elucidations cannot be fully understood without first formally defining/elucidating ‘temporal instant’ and ‘temporal interval’.
- I propose the following elucidation.

Elucidation: Temporal Instant is an Occurrent having no temporal extent.

Examples (borrowed from the BFO documentation): right now; the moment at which a finger is detached in an industrial accident; the moment at which a child is born; the moment of death - I propose the following elucidation.

Elucidation: Temporal Interval is an Occurrent bounded by two Temporal Instants.

Examples: The Macy’s Christmas Parade temporally bounding of 9:00 AM EST to 12:00 PM EST; the start & finish times that temporally bound a relay race - I propose the following axiom.

Axiom: A Temporal Interval contains two or more Temporal Instants as parts. - I propose the following elucidation.

Elucidation: A One-Dimensional Temporal Region is a Temporal Region which parts are wholly contained by one or more Temporal Intervals and/or Temporal Instants. - I propose the following elucidation.

Elucidation: A Contiguous One-Dimensional Temporal Region is a One-Dimensional Temporal Region which parts are wholly contained within a single Temporal Interval.

Example: The start & end times that temporally bound a television episode viewing, whereby the viewing occurs without pause and/or interruption, such as would occur in a streamed playback without commercial ads or where the viewer does not pause viewing or step away from viewing at any time during the episode’s playback. - I propose the following elucidation.

Elucidation: A Discontiguous One-Dimensional Temporal Region is a One-Dimensional Temporal Region which parts are wholly contained within one or more non-contiguous Temporal Intervals.

Example: The start & end times that temporally bound a television episode viewing, whereby the viewing occurs with one ore more pauses and/or interruptions, such as would occur in a streamed playback with commercial ad interruptions, pausing episode playback to answer a telephone call, walking away from a live broadcast to answer the door, etc. - I propose the following axiom.

Axiom: A Contiguous One-Dimensional Temporal Region contains two or more contiguous Temporal Instants bounded by a single Temporal Interval. - I propose the following axiom.

Axiom: A Discontiguous One-Dimensional Temporal Region is bounded by two or more non-contiguous Temporal Intervals, whereby one or more of these Temporal Intervals may bound two or more non-contiguous Temporal Instants. - I propose, just as Object Aggregate is both a Material Entity and pairwise disjoint with Object and Fiat Object Part, that Temporal Instant and Temporal Interval become direct subtypes of Occurrent and are made pairwise disjoint with Process, Process Boundary, Temporal Region, and Spatiotemporal Region.

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Lastly, the (DRAFT) BFO-2020 documentation states the following:

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“Since temporal regions are temporal parts (though not temporal proper parts) of themselves, this means, in particular, that zero-dimensional temporal regions (temporal instants) are also occurrents.”

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Consistent with the BFO 2.0 documentation, the preceding sentence infers a synonymous equivalence between ‘zero-dimensional temporal region’ and ‘temporal instant’. The two are not the same. Rather, a ‘zero-dimensional temporal region’ particular is a collection of one or more ‘temporal instant’ particulars, as follows from A.1.2.75. The preceding (DRAFT) BFO-2020 statement conflates these terms. A ‘zero-dimensional temporal region’ cannot be the same as a ‘temporal instant’, even if a ‘zero-dimensional temporal instant’ particular contains a single ‘temporal instant’ particular. More broadly, a collection is not the same as that which the collection contains.

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Regards,

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Anthony

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