1 VT 2 Ontology and Ontologies Barry Smith 3 IFOMIS Strategy get real ontology right first and then...
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Transcript of 1 VT 2 Ontology and Ontologies Barry Smith 3 IFOMIS Strategy get real ontology right first and then...
1
VT
2
Ontology and Ontologies
Barry Smith
3
IFOMIS Strategy
get real ontology right first
and then investigate ways in which this real ontology can be translated into computer-
usable form later
NOT ALLOW ISSUES OF COMPUTER-TRACTABILITY TO DETERMINE THE
CONTENT OF ONTOLOGY
4
BFO
Basic Formal Ontology (BFO)
BFO as an ontological theory of reality designed as a real constraint on domain ontologies
5
Reality
6
is complicated
7
What is the best language to describe this complexity?
8
Unfortunately
… there are problems with the use of English as a formal representation language
9
Nouns and verbs
Substances and processes
Continuants and occurrents
In preparing an inventory of reality
we keep track of these two different categories of entities in two different ways
10
Natural language
glues them together indiscriminately
substance
t i m
e
process
11
SNAP vs. SPAN(roughly: Snapshot vs. Video)
substance
t i m
e
process
12
SPAN Ontology of Processes unfolding (messily) in time
t i m e
13
Substances and processes
t i m
e
process
demand different sorts of inventories
14
Substances demand 3-D partonomies
space
15
Processes demand 4D-partonomies
t i m e
16
Substances have spatial parts
17
Processes have temporal parts
The first 5 minutes of my headache is a temporal part of my headache
The first game of the match is a temporal part of the whole match
18
Substances do not have temporal parts
The first 5-minute phase of my existence is not a temporal part of me
It is a temporal part of that complex process which is my life
19
You are a substance
Your life is a process
You are 3-dimensional
Your life is 4-dimensional
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Two alternative basic ontologies
SNAP and SPAN
SNAP = substances plus qualities, functions, roles, conditions, etc.
SPAN = processes
21
These represent two views
of the same rich and messy reality
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SNAP: Time-Stamped Ontologies
t1
t3t2
here time exists outside the ontology, as an index or time-stamp
23
24
SPAN: Here time exists within the
ontology itself
t i m e
25
Three views/partitions of the same reality
26
BFO’s two main components
1. SNAP and SPAN
2. The Theory of Granular Partitions
27
Theory of granular partitions
• There is a projective relation between cognitive subjects and reality
Major assumptions:
• Humans see reality as through a grid
• The grid is usually not regular and raster shaped
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Projection of cells
…
Wyoming
Idaho
Montana
…
Cell structure North AmericaProjection
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Ontological Zooming
medicine
cell biology
30
Ontological Zooming
distinct partitions of one and the same reality
31
When viewing reality
in terminology systems, maps, inventories, descriptions, or in simple perception and reasoning
WE ALWAYS CHOOSE SOME LEVEL OF GRANULARITY AT WHICH TO WORK
32
Projective relation to reality
33
Crisp and vague projection
…Montana
…
crisp
The Himalayas
EverestvagueP1
Pn
34
Theory of granular partitionsMajor assumptions
– Projection is an active process:
• it brings certain features of reality into the foreground of our attention (and leaves others in the background)
– The projective relation can reflect the mereological structure of reality
35
Projection of cells (1)
Cell structure Targets in reality
Hydrogen
Lithium
Projection
36
Projection of cells (2)
…
Wyoming
Idaho
Montana
…
Cell structure North AmericaProjection
37
Multiple ways of projecting
CountypartitionHighwaypartition
Big citypartition
38
Two core components of the theory of granular partitions
– Cell structures (Theory A)– Projective relation to reality (Theory
B)
39
Theory ACells and Subcells
40
Species Genera as Tree
canary
animal
bird fish
ostrich
41
Species-Genera as Map/Partition
animal
bird
canary
ostrich
fish
canary
42
Systems of cells
• Subcell relation– Reflexive, transitive, antisymmetric
The cell structure of a granular partition has a unique maximal cell (top-most node, root)
Each cell is connected to the root by a finite chain
Every pair of cells stands either in a subcell or a disjointness relation (tree structure)
43
Theory BProjection of Cells onto Reality
44
Projection and location
H u m a ns A p es U n ico rns
M a m m a ls
Humans Apes
Dogs
Mammals
),Humans''( HumansP
lysuccessfulproject
NOT does Unicorn'' cell The
???),'Unicorn(' P
recognized
NOT is species The
???)L(Dogs,
Dog
)Humans'',(HumansL
45
Misprojection
…
Montana
Wyoming
…
P(‘Montana’,Montano) and L(Montana,’Montana’)
P(‘Wyoming’,Sicily) but not L(Sicily,’Wyoming’)
46
A granular partition projects transparently onto reality if and only if
Transparency of projection (1)
– Location presupposes projectionL(o,z) P(z,o)
– There is no misprojectionP(z,o) L(o,z)
47
Transparency of projection (2)
Still: there may be irregularities of correspondence
– There may be cells that do not project (e.g. ‘unicorn’)
– Multiple cells may target the same object
– There may be ‘forgotten’ objects (e.g. the species dog above)
48
Functionality constraints (1)
Morning Star
Evening StarVenus
Location is functional: If an object is located in two cells then these cells are identical, i.e., L(o,z1) and L(o,z2) z1 = z2
Two cells projecting onto the same object
49
Functionality constraints (2)
China
Republic of China(Formosa)
People’s Republic of China
The same name for two different things:
Projection is functional: If two objects are targeted by the same cell then they are identical, i.e., P(z,o1) and P(z,o2) o1 = o2
50
Morning Star/Evening Star/Venus and other problems solved
by providing a formal framework for dealing with the ways in which partitions are refined and corrected with increases in our knowledge
about misprojections
about ambiguity
about multiple terms designating the same object
about hitherto unknown objects/types
51
Preserve mereological structure
Helium
Noble gases
Neon
EmptyNeonHelium
gasesNobleNeon
gasesNobleHelium
EmptyNeHe
NGNe
NGHe
Potential of preserving mereological structure
52
Partitions should not distort mereological structure
M am m als A p es U n ico rn s
H u m an s
Humans Apes
Dogs
Mammals
HumansMammal
Humans''Mammal''
distortion
If a cell is a proper subcell of another cell then the object targetedby the first is a proper part of the object targeted by the second.
53
Features of granular partitions
• Selectivity– Only a few features are in the foreground of
attention
• Granularity– Recognizing a whole without recognizing all of
its parts
• Preserve mereological structure
54
Classification of granular partitions
according to
• Degree of preservation of mereological structure
• Degree of completeness of correspondence
• Degree of redundancy
55
Mereological monotony
…
Helium
Noble gases
Neon
…
Helium
Noble gases
Neon
Projection does not distort mereological structure
21212,21,1 o and )( and )( zzozoLzoL Projection preserves mereological structure
56
Projective completeness
Empty cells
function totala is Projection
scompletnes Projective
),(:),( zoLoAzZ
Every cell has an objectlocated within it:
57
Exhaustiveness
Humans Apes
Dogs
Mammals
Everything of kind in the domain of the partition A is recognized by some cell in A
),( and ),(:
and )(
zoLAzZz
Φ(o)ADo
Humans Apes Cats
Mammals
58
Science= the endeavour to construct partitions of reality
which satisfy the conditions of
mereological monotony (tree structure)
exhaustiveness (every object recognized)
functionality (one object per cell)
…but no God’s eye partition
– every partition we create has some granularity