The Cornucopia of FormalOntological Relations
Barry Smith and Pierre Grenon
Institute for Formal Ontology and Medical
Information Science
1
Realist Perspectivalism
There is a multiplicity of ontological
perspectives on reality, all equally
veridical i.e. transparent to reality
2
Anatomy vs. Pathology
3
The Problem
The tumor developed in John’s lung
over 25 years
4
The Problem
____ developed in _____ over 25 years
process
state
5
The Problem
The tumor developed in the lung over 25 years
substances
things
objects
continuants
6
The Problem
The tumor developed in John’s lung over
25 years
PARTHOOD NOT DETERMINATE
7
The Problem
The tumor developed in the lung over 25 years
substances
processes
GLUING THESE TOGETHER YIELDS
ONTOLOGICAL MONSTERS
8
Substances and processes
exist in time in different ways
process
substance
9
SNAP vs SPAN
Endurants vs perdurants
Continuants vs occurrents
In preparing an inventory of reality
we keep track of these two different
kinds of entities in two different ways
10
Need for different perspectives
Not one ontology, but a multiplicity of
complementary ontologies
Cf. particle vs. wave ontologies in
quantum mechanics
11
Three kinds of SNAP entities
1. Substances
2. Dependents (SPQR… entities)
3. Spatial regions, contexts,
niches, environments
12
SPQR… entities
States, powers, qualities, roles …
functions, dispositions, plans,
shapes, status, habitus, liabilities …
= dependent SNAP entities
13
SPQR… entities:
one-place:
your temperature, color, height
my knowledge of French
the whiteness of this cheese
the warmth of this stone
the fragility of this glass
14
relational SPQR… entities
stand in relations of one-sided dependence
to a plurality of substances simultaneously
love
specific dependence
John
Mary
15
Generic dependence of relational
SPQR… entities
legal systems
languages (as systems of competences)
religions (as systems of beliefs)
16
Three kinds of SNAP entities
1. Substances
2. Dependents (SPQR… entities)
3. Spatial regions, contexts,
niches, environments
17
Three kinds of SNAP entities
1. Substances
2. Dependents (SPQR… entities)
3. Spatial regions, contexts,
niches, environments
18
Spatial regions, contexts, niches,
environments
Organism species evolve into
environments
Domesticated spatial regions: rooms,
nostrils, your alimentary tract
Fiat spatial regions: JFK designated
airspace
19
SNAP: Entities existing in toto at a time
M edO
D ra ft 0 .0 0 0 4
E n d u rin g E n tity
[E xists in sp a ce a n d tim e ,
h a s n o te m p o ra l p a rts]
D e p e n d e n t E n tity
[ ± R e la tio n a l]
S p a tia l E n tity
O ccu p ie d
U n o ccu p ie d
Q u a lity
[S o m e tim e s fo rm q u a lityre g io n s o r sca le s]
Tunnel
A lim e n ta ry C a n a l
S p a tia l re g io n o f 3
d im e n sio n s
o ccu p ie d b y o rg a n ism
S p a tia l re g io n o f 2
d im e n sio n s *
o ccu p ie d b y b u rn , b ru ise
SNAP
H o llo w
N o stril
C a vity
In te rio r o f L u n g
R e q u isite
[H a ve d e te rm in a b le /
d e te rm in a te stru ctu re ]
T e m p e ra tu re . h e ig h t
O p tio n a l
D ia b e te s
S ta te
B e in g p re g n a n t, b e in g th irsty
In d e p e n d e n t E n tity
R o le , F u n ctio n , P o w e r, D isp o sitio n
[H a ve re a liza tio n s, ca lle d p ro ce sse s]
T o c ircu la te b lo o d , to se cre te h o rm o n e s
S u b sta n ce
O rg a n ism , o rg a n
F ia t p a rt o f su b sta n ce *
E xtre m ity, u p p e r b o d y
B o u n d a ry o f su b sta n ce *
S u rfa ce o f skin o r h id e
A g g re g a te o f su b sta n ce s *
F a m ily, m o th e r a n d fe tu s
20
NAP
In d e p e n d e n t E n tity
R o le , F u n ctio n , P o w e r, D isp o sitio n
[H a ve re a liza tio n s, ca lle d p ro ce sse s]
T o c ircu la te b lo o d , to se cre te h o rm o n e s
Substances
S u b sta n ce
O rg a n ism , o rg a n
F ia t p a rt o f su b sta n ce *
E xtre m ity, u p p e r b o d y
B o u n d a ry o f su b sta n ce *
S u rfa ce o f skin o r h id e
A g g re g a te o f su b sta n ce s *
F a m ily, m o th e r a n d fe tu s
21
.0 0 0 4
E n d u rin g E n tity
[E xists in sp a ce a n d tim e ,
h a s n o te m p o ra l p a rts]
SNAP
D e p e n d e n t E n tity
[ ± R e la tio n a l]
Q u a lity
[S o m e tim e s fo rm q u a lityre g io n s o r sca le s]
R e q u isite
[H a ve d e te rm in a b le /
d e te rm in a te stru ctu re ]
T e m p e ra tu re . h e ig h t
S ta te
B e in g p re g n a n t, b e in g th irsty
R o le , F u n ctio n , P o w e r, D isp o sitio n
[H a ve re a liza tio n s, ca lle d p ro ce sse s]
T o c ircu la te b lo o d , to se cre te h o rm o n e s
O p tio n a l
D ia b e te s
SPQR …
22
S p a tia l E n tity
O ccu p ie d
Spatial
regions
U n o ccu p ie d
Qu
[S o m e tim e s
re g io n s
Tunnel
A lim e n ta ry C a n a l
S p a tia l re g io n o f 3
d im e n sio n s
o ccu p ie d b y o rg a n ism
S p a tia l re g io n o f 2
d im e n sio n s *
o ccu p ie d b y b u rn , b ru ise
H o llo w
N o stril
R e q u isite
[H a ve d e te rm in a b le /
d e te rm in a te stru ctu re ]
T e m p e ra tu re . h e ig h t
C a vity
In te rio r o f L u n g
23
The SPAN Ontology
time
24
The SPAN ontology
here time exists as part of the
domain of the ontology
25
mereology works without
restriction everywhere here
clinical trial
time
26
Processes, too, are dependent
on substances
One-place vs. relational processes
One-place processes:
your getting warmer
your getting hungrier
27
Examples of relational
processes
kissings, thumpings, conversations,
dancings,
join their carriers together into
collectives of greater or lesser
duration
28
SPAN: Entities extended in
time
Entity extended in time
Processual Entity
[Exists in space and time, unfolds
in time phase by phase]
Portion of Spacetime
Spacetime worm of 3 + T
dimensions
occupied by life of organism
Temporal interval *
projection of organism’s life
onto temporal dimension
SPAN
Process
[±Relational]
Circulation of blood,
secretion of hormones,
course of disease, life
Fiat part of process *
First phase of a clinical trial
Aggregate of processes *
Clinical trial
Temporal boundary of
process *
onset of disease, death
29
Two kinds of SPAN entities
1. Processes (including events:
process-boundaries)
2. Spatio-temporal regions
30
Processes
Entity extended in time
SPAN
Processual Entity
[Exists in space and time, unfolds
in time phase by phase]
Process
[±Relational]
Circulation of blood,
secretion of hormones,
course of disease, life
Fiat part of process *
First phase of a clinical trial
Aggregate of processes *
Clinical trial
Temporal boundary of
process *
onset of disease, death
31
Spatio-temporal
regions
Entity extende
Portion of Spacetime
Proce
Spacetime worm of 3 + T
dimensions
occupied by life of organism
Temporal interval *
projection of organism’s life
onto temporal dimension
[±Relatio
Circulation o
secretion of h
course of dis
32
4-dimensional environments
Lobsters have evolved into
environments marked by cyclical
patterns of temperature change
Tudor England
The Afghan winter
The window of opportunity for an
invasion of Iraq
33
How do you know whether an
entity is SNAP or SPAN?
34
problem cases
forest fire
anthrax epidemic
hurricane Maria
traffic jam
ocean wave
35
forest fire:
a process
a pack of monkeys jumping from tree to
tree and eating up the trees as they go
the Olympic flame:
a process or a thing?
(anthrax spores are little monkeys)
36
Formal-ontological concepts
come for free
do not add anything to being
are domain-independent
are expressed linguistically by closedclass items …
HOW TO GENERATE THEM?
37
The idea (first rough version)
Formal relations are those relations
which are not captured by either
SNAP or SPAN
because they traverse the SNAPSPAN divide
they glue SNAP and SPAN entities
together
38
This generates a first list of formal
relations,
e.g. dependence,
but we find some of these relations
also within SNAP or within SNAP
39
The idea (modified version)
Formal relations are the relations that
hold SNAP and SPAN
entities/ontologies together
and analogous relations
40
Example:
Individuation, segmentation
41
Substances
tokens separated by bona fide
boundaries
form natural kinds, types
(universals, species + genera)
separated by bona fide boundaries
42
Processes
Process tokens merge into one another
Process kinds merge into one another
… few clean joints either between
tokens or between types
43
boundaries are mostly fiat
everything is flux
time
44
SNAP entities
provide the principles of
individuation/segmentation for SPAN
entities
No change without some THING or
QUALITY which changes
45
Example:
Ontological Dependence
(SPAN, SNAP): process  substance
The erosion of the rock necessitates the
existence of the rock
(SNAP, SNAP): SPQR  substance
The token redness of the sand
necessitates the existence of the sand
46
Generating a typology
Two main types of formal relations:
meta-ontological: obtain between
entities of different ontologies
intra-ontological: obtain between
entities of the same ontology (intraSNAP, intra-SPAN)
47
Three parameters:
- the arity of the relation
- the types of the relata, expressed as
an ordered list, called the signature of
the relation
- the formal nature of the relation
48
Principal Signatures
In the binary case:
SNAP-SNAP
- (SNAPi, SNAPi), i = i
- (SNAPi, SNAPi), i < j, i > j
SPAN-SPAN
SNAP-SPAN
SPAN-SNAP
49
Transtemporal relations
Examples:
Genidentity
(transtemporal generalization of
identity/part-whole)
Successive causality
50
Genidentity
The such-has-to-have-come-forth-from relation.
Signature: SNAPi-SNAPj
Cut a chunk of matter in two, the sum of the
remaining pieces is genidentical to the chunk
before cutting
Also SPAN-SPAN? Is there a form of genidentity
among processes?
51
Successive Causality
SPAN-SPAN: Process causation
One process causes another process
SPAN-SNAP: Causal repercussion
A process results in the modification of a substance
(always mediated by process causation)
SNAP-SPAN: Agent causation
A substance produces causally a process
SNAP-SNAP: Causal origin
One substance is the causal origin of another
(mediated by other types of causal relations)
52
Successive Causality
SPAN-SPAN: Process causation
SPAN-SNAP: Causal repercussion
SNAP-SPAN: Agent causation
SNAP-SNAP: Causal origin
do not apply on all
levels of granularity
(holds of examples
given below also)
53
Our main target:
Temporally extended relations
Simultaneous Causality
Participation
(holds between a substance and a
process such as an action or a life or
history)
Realization
(holds between SPQR… entities and their
SPAN expressions)
54
Simultaneous causality
SPAN-SPAN
The rise in temperature causes the
(simultaneous) increase in pressure
(Boyle’s law)
55
Substance  Process
PARTICIPATION
(a species of dependence)
56
Participation (SNAP-SPAN)
A substance (SNAP) participates in a
process (SPAN)
A runner participates in a race
A voter participates in an election
57
Participation
B
x
y
time
SNAP-ti.
SPAN
substances x, y participate in process B
slice of
x’s life
58
Axes of variation
activity/passivity (agentive)
direct/mediated
benefactor/malefactor
(conducive to existence) [MEDICINE]
59
SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Termination
Perpetuation
Influence
Patiency
(-agentive)
Facilitation
Hindrance
Mediation
60
Perpetration
A substance perpetrates an action
(direct and agentive participation in a
process):
The referee fires the starting-pistol
The captain gives the order
61
Initiation
A substance initiates a process:
The referee starts the race
The attorney initiates the process of
appeal
62
Perpetuation
A substance sustains a process:
The singer sings the song
The charged filament perpetuates the
emission of light
63
Termination
A substance terminates a process:
The operator terminates the projection
of the film
The judge terminates the imprisonment
of the pardoned convict
64
Influence
A substance (or its quality) has an
effect on a process
The steepness of the slope affects
the movement of the troops
The politicians influence the course of
the war
65
Facilitation
A substance plays a secondary role in a
process (for example by participating in a
part or layer of the process)
The catalyst provides the chemical
conditions for the reaction
The traffic-police facilitate our rapid
progress to the airport
66
Facilitation
is this really a binary relation?
67
Hindrance, prevention, inhibition
A substance has a negative effect on the
unfolding of a process (by participating in
other processes)
The drug hinders the progression of the
disease
The strikers prevent the airplane from
departing
68
Hindrance, prevention, inhibition
Is this really a binary relation ? (What is
the second term?)
69
Mediation
A substance plays an indirect role in the
unfolding of a process relating other
participants:
The Norwegians mediate the
discussions between the warring parties
70
Patiency
Dual of agentive participation
John kisses [Mary] (John agent)
Mary is kissed [by John] (Mary patient)
71
Signatures of meta-relations
SNAP Component
Substances
SPQR…
SPAN Component
Processuals
Processes
Events
Space Regions
Space-Time Regions
72
Signatures of meta-relations
SNAP Component
Substances
SPQR…
SPAN Component
Processuals
Processes
Events
Space Regions
Space-Time Regions
73
Signatures of meta-relations
SNAP Component
Substances
SPQR…
SPAN Component
Processuals
Processes
Events
Space Regions
Space-Time Regions
74
Signatures of meta-relations
SNAP Component
Substances
SPQR…
SPAN Component
Processuals
Processes
Events
Space Regions
Space-Time Regions
75
REALIZATION
76
Signatures of meta-relations
SNAP Component
Substances
SPQR…
SPAN Component
participation
Processuals
Processes
Events
Spatial Regions
Space-Time Regions
77
Realization (SPQR  process)
The most general relation between a
dependent (SPQR…) entity and a process
The power to legislate is realized through
the passing of a law
The role of antibiotics in treating infections
is via the killing of bacteria
78
Realization (SNAP-SPAN)
the execution of a plan,
algorithm
the expression of a function
the exercise of a role
the realization of a disposition
79
SPQR… entities and their SPAN
realizations
plan
function
role
disposition
algorithm
SNAP
80
SPQR… entities and their SPAN
realizations
execution
expression
exercise
realization
application
course
SPAN
81
Material examples:
performance of a symphony
projection of a film
expression of an emotion
utterance of a sentence
application of a therapy
course of a disease
increase of temperature
82
SNAP  SPAN
Participation
Substance  Process
Realization
SPQR  Process
83
SPAN  SNAP
Involvement
84
SPAN  SNAP
Involvement
Creation
Sustaining in being
Degradation
Destruction
Blurring
Demarcation
85
Involvement
process  substance
(sometimes the converse of participation):
Races involve racers
(but not always):
Wars involve civilians
86
Creation
A process brings into being a substance:
The declaration of independence
creates the new state
The work of the potter creates the vase
87
Sustaining in being
A process sustains in being a
substance:
The circulation of the blood sustains
the body
Levying taxes sustains the army
88
Degradation
A process has negative effects upon a
substance
Eating sugar contributes to the
deterioration of your teeth.
The flow of water erodes the rock
89
Destruction
A process puts a substance out of
existence
The explosion destroys the car
The falling of the vase on the floor
breaks it
90
Demarcation
A process creates (fiat or bona fide)
boundaries of substances.
The signing of the treaty establishes fixed
borders between the two nations
The tracing of the area of operation by the
surgeon defines a boundary, the incision
performed by the surgeon yet another one
91
Blurring
A process destroys boundaries of
substances:
The military stand-off creates the no man's
land
The successful transplant obliterates the
boundary between original and grafted
tissue
92
Process  SPQR
Qualitative projection
Creation
Continuation
Destruction
Degradation
93
Qualitative Projection
A warming process yields a rise in
temperature
The tenure process yields a rise in
John’s status
94
Creation
A process brings into being a dependent
entity
The accident reshapes the car.
The baking of the clay gives the vase
its rigidity and color.
95
Continuation
A process sustains the existence of an
SPQR entity
The firing of the fireworks maintains the
coloration of the sky
The intake of alcohol sustains the rosiness
of his cheeks
96
Degradation
A process affects a substance's quality
or status by lowering its degree
The opening of the window
diminishes the temperature in the
room
97
Destruction
A process destroys/changes an SPQR…
entity
The accident destroys the car's shape
The burning of the vase destroys its color
The demotion relieved him of his rank as an
officer
98
Varieties of projection
Warming process  series of
temperature qualities
= qualitative projection
Process  temporal interval
= temporal projection
99
Spatial Projection
A process occurs in a given place or
area:
The Revolution took place in Paris
The wind blows beyond the 24th
parallel
100
Starts in / ends at
(spatial projection of process
boundaries)
A process begins/ends at a location
The race started in Paris
The race ended in Roubaix
101
SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Termination
Perpetuation
Influence
Patiency
(-agentive)
Facilitation
Hindrance
Mediation
102
SPAN-SNAP
Qualitative projection
Creation
Involvement
Creation
Continuation
Destruction
Degradation
Sustenance
Degradation
Destruction
Blurring
Demarcation
103
Varieties of Projection
A process projects
onto its temporal duration,
onto the spatio-temporal region it occupies
onto the spatial region it occupies at a
given time
onto the sum of its participants at a time
onto the sum of the SPQR… entities
realized through it at a time
104
Temporal Projection
of SPAN entities onto temporal
intervals
of SNAP entities onto temporal
intervals via their lives
105
Formal relations not dealt with so far:
part-whole
instantiation
reference, intentionality
truthmaking
106
Part-Whole
Basic relation exclusively intraontological: either SNAP-SNAP or
SPAN-SPAN.
SNAP-SNAP: only if SNAPis have
the same temporal index
107
Relations crossing the SNAP/SPAN
border are never part-relations
substance John
John’s life
physiological
processes
108
Granularity
spatial region
substance
parts of substances are always substances
109
Granularity
spatial region
substance
parts of spatial regions are always spatial regions110
Granularity
process
parts of processes are always processes111
Intra-granular and cross-granular
parthood
across SNAPs:
Kevin’s arm is part of Kevin
Kevin’s molecule is part of Kevin
across SPANs:
Kevin’s leg-movement is part of Kevin’s
running
Kevin’s cytometabolism is part of Kevin’s
running
112
The idea (a further modification)
Formal relations are those relations
which are not captured by either the
SNAP or the SPAN ontology
either because they can traverse the
SNAP-SPAN divide
or because they can traverse the
granular divide
113
Is this Kantianism?
does every ontology/perspective
generate new formal-ontological
relations?
114
Realist Perspectivalism
There is a multiplicity of ontological
perspectives on reality, all equally
veridical i.e. transparent to reality
115
SNAP
M edO
D ra ft 0 .0 0 0 4
E n d u rin g E n tity
[E xists in sp a ce a n d tim e ,
h a s n o te m p o ra l p a rts]
D e p e n d e n t E n tity
[ ± R e la tio n a l]
S p a tia l E n tity
O ccu p ie d
U n o ccu p ie d
Q u a lity
[S o m e tim e s fo rm q u a lityre g io n s o r sca le s]
Tunnel
A lim e n ta ry C a n a l
S p a tia l re g io n o f 3
d im e n sio n s
o ccu p ie d b y o rg a n ism
S p a tia l re g io n o f 2
d im e n sio n s *
o ccu p ie d b y b u rn , b ru ise
SNAP
H o llo w
N o stril
C a vity
In te rio r o f L u n g
R e q u isite
[H a ve d e te rm in a b le /
d e te rm in a te stru ctu re ]
T e m p e ra tu re . h e ig h t
O p tio n a l
D ia b e te s
S ta te
B e in g p re g n a n t, b e in g th irsty
In d e p e n d e n t E n tity
R o le , F u n ctio n , P o w e r, D isp o sitio n
[H a ve re a liza tio n s, ca lle d p ro ce sse s]
T o c ircu la te b lo o d , to se cre te h o rm o n e s
S u b sta n ce
O rg a n ism , o rg a n
F ia t p a rt o f su b sta n ce *
E xtre m ity, u p p e r b o d y
B o u n d a ry o f su b sta n ce *
S u rfa ce o f skin o r h id e
A g g re g a te o f su b sta n ce s *
F a m ily, m o th e r a n d fe tu s
universals and particulars
116
What about
reference, intentionality,
truthmaking ?
117
S
d
Me
O
Dr
0 .0
a ft
a ti
En
al
a li ty
a li ty
qu
Qu
m
s]
fo r
es
c a le
ti m
r s
me
s o
io n
[S o
re g
ti ty
occ
ie d
A li
f 3
n o
g io
l re
ns
is m
s io
a ti a
an
en
o rg
d im
by
ie d
p
ccu
up
el
l
nn
na
Tu
Ca
ry
n ta
me
in g
-
al
ti o n s
Op
te
be
D ia
ie d
p
n
re g
In d
ep
en
de
nt
En
ti ty
nce
n
b s ta o rg a
Su
,
is m
an
O rg
io n
o s it e s ]
is p
ss
es
r, D
ce
on
w e d p ro
rm
Po
ho
n,
a ll e
te
c ti o n s , c
c re
un
e
o
F
s
a ti
to
le ,
a li z
d,
Ro
o
re
b lo
ve
te
[H a
c u la
c ir
To
s ty
*
nce
b s ta o d y
su
r b
of
pe
a rt
up
t p
it y ,
F ia
m
tr e
Ex
*
nce
s ta
e
sub
h id
of
or
ry
da
s k in
un
of
Bo
ce
rf a
u
S
s *
nce s
s ta
tu
sub
d fe
of
an
te
er
ga
o th
g re
Ag
y, m
il
m
Fa
e
/
is it
b le
qu
in a
Re
re ]
te rm u c tu
de
t
s tr
ve
ig h
te
he
[H a
in a
e
r .
te rm ra tu
de
e
p
m
Te
ll o w
Ho
il
s tr
No
Sp
o
4
ir
te
g th
S ta
e in
t, b
an
Un
cup
e,
n ti ty
g E n d ti m
ri n
]
a
du
ce
a r ts
En
s p a o ra l p
p
ts in
m
is
o te
[E x
s n
a
n ti ty
h
t E
en
al ]
nd
ti o n
pe
D e R e la
[±
Be
Sp
Oc
00
P
NA
In te
v it y
g
un
Ca
f L
r o
ri o
f 2
n o
g io
*
e
a l re io n s
ru is
a ti
s
, b
en
urn
d im
y b
d b
ie
cup
Sp
oc
118
Puzzle
Are there any cases of ontological dependence
involving an increase in being,
analogous to the increase in being between the
thought and the thinker, the charge and the
conductor, the swim and the swimmer
between SPAN and SPAN entities?
(Hypothesis: all qualities of processes are
essential)
119
Co-temporality
is a requisite for most SNAP-SPAN
relations (participation, realization,
etc.)
Exception:
the memory of a process
state of memory: SNAP
(vs. episodic remembering: SPAN)
120
Descargar

Formal Ontology - University at Buffalo