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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> 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:
“A temporal interval is a special kind of one-dimensional temporal region, namely one that is self-connected (is without gaps or breaks).”
BFO-2020 offers the following elucidations:
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.
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.
I made some observations under separate cover, which I will summarize here.
Lastly, the (DRAFT) BFO-2020 documentation states the following:
“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.”
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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