1. Permanent Generic Relatedness
Niels Grewe, Ludger Jansen, Barry Smith
FOIS Ontology Competition 2016

2. Every portion of skin tissue has a Keratinocyte (kcyte) as part
kcyte =def. an epidermal cell which produces keratin

3. permanent specifical relatedness (PSR)
SkinTissue
(x)
Kcyte
(y)
has_part
exists_at
exists_at
[t0…tn]
same relatum, all the time
works for your brain

4. temporary relatedness (TR)
SkinTissue
(x)
Kcyte
(y)
has_part
exists_at
exists_at
[tm…tn-1]
[t0…tn]
same relatum, but only for part of the time
works for milk teeth

5. permanently, generically related (PGR)
Every portion of skin tissue contains a Kcyte at every time in its history but not necessarily the same one
has_part
SkinTissue
(x)
Kcyte
(y1)
Kcyte
(y2)
exists_at
exists_at
exists_at
[t0…tm]
[tm…tn]
[t0…tn]
permanently, generically related (PGR)
instance level change is silent on the type level

6. FOL Translations BFO 2 (Permanent Specific Relatedness - PSR)
t s (SkinTissue(s,t)  k Kcyte (s has_part k at t))
BFO 2 (Temporary Relatedness - TR)
t s (SkinTissue(s,t)  t k (t continuant_part_of t
& Kcyte(k) & (s has_part k at t))
BFO 2 (Permanent Generic Relatedness - PGR)
t s (SkinTissue(s,t)  t ((t continuant_part_of t & TimeInstant(t))  k (Kcyte(k) & s has_part k at t))

7. OWL 2 Translations ??? Naive (ambiguous)
SkinTissue SubclassOf has_part some Kcyte
BFO 2 (PSR)
SkinTissue SubclassOf has_continuant_part_at_all_times some Kcyte
BFO 2 (TR)
SkinTissue SubclassOf has_continuant_part_at_some_time some Kcyte
BFO 2 (PGR)
???

8. BFO 2 History Process (p) Object (o) History_of relation
Unfolds over a period of time
Has temporal parts
Examples: The life of an organism
Object (o)
Occupies a unique BFO spatiotemporal region r(o)
History_of relation
history_of (p, o): p = sum of all processes occurring in r(o)
Provides a 1–1 link between object and process

9. Using parts of histories to represent PGR
PGR allows different relata at different times
Continuants cannot have temporal parts
But histories can have temporal parts (has_proper_occurrent_part)

10. Phases of histories
Continuant
has_history
History
Phase
has_proper_
occurrent_part
A phase is a temporal part of the history of a continuant
The phases are parts of a process sum pertaining to a single entity

11. Phases and TQCs
TQC_of
Continuant
TQC
has_history
phase_of
History
Phase
has_proper_
occurrent_part
Each phase projects onto what we can think of as a temporally qualified continuant (~ the continuant as if it only existed during that phase)

12. HasKcytePartPhase HasKcytePartPhase EquivalentTo (
(has_proper_occurrent_part some
HasKcyte-PartPhase)
and
(has_proper_occurrent_part only HasKcytePartPhase) ) or
(phase_of some (has_continuant_part_at_all_times
some Kcyte))

13. Translation x is a HasKcytePartPhase 
either x is composed exclusively and non-vacuously of HasKcytePartPhases,
or x is a phase of an entity that has a Kcyte as part at all times

14. Permanent Generic Relatedness
SkinTissue SubclassOf has_history some HasKcytePartPhase
The history of any portion of skin tissue is a continuous sequence of HasKcytePartPhases of varying length

15. (y1) (y2) (y3) HKPPhase@[t0…tn] HKPPhase @[tm…tn] HKPPhase @[t0…tm]
SkinTissue
(x1)
has_phase
has_occurrent_part
has_occurrent_part
Kcyte
(y1)
SkinTissue_TQC(x2)
phase_of
continuant _part_of_at _all_times
has_occurrent_part
Kcyte
(y2)
SkinTissue_TQC(x3)
phase_of
continuant _part_of_at _all_times
Kcyte
(y3)
SkinTissue_TQC(x4)
phase_of
continuant _part_of_at _all_times

16. Conclusion can be captured in an OWL 2 setting
retains compatibilist 3D/4D view of BFO
high complexity, partially mitigated through tool support (Tawny OWL macros)
TQCs can be viewed as part of a model of BFO 2 OWL (as a façons de parler)