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VT

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Ontology and Ontologies

Barry Smith

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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

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BFO

Basic Formal Ontology (BFO)

BFO as an ontological theory of reality designed as a real constraint on domain ontologies

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Reality

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is complicated

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What is the best language to describe this complexity?

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Unfortunately

… there are problems with the use of English as a formal representation language

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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

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Natural language

glues them together indiscriminately

substance

t i m

e

process

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SNAP vs. SPAN(roughly: Snapshot vs. Video)

substance

t i m

e

process

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SPAN Ontology of Processes unfolding (messily) in time

t i m e

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Substances and processes

t i m

e

process

demand different sorts of inventories

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Substances demand 3-D partonomies

space

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Processes demand 4D-partonomies

t i m e

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Substances have spatial parts

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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

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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

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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

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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

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SPAN: Here time exists within the

ontology itself

t i m e

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Three views/partitions of the same reality

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BFO’s two main components

1. SNAP and SPAN

2. The Theory of Granular Partitions

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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

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Ontological Zooming

distinct partitions of one and the same reality

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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

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Projective relation to reality

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Crisp and vague projection

…Montana

…

crisp

The Himalayas

EverestvagueP1

Pn

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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

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Projection of cells (1)

Cell structure Targets in reality

Hydrogen

Lithium

Projection

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Projection of cells (2)

…

Wyoming

Idaho

Montana

…

Cell structure North AmericaProjection

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Multiple ways of projecting

CountypartitionHighwaypartition

Big citypartition

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Two core components of the theory of granular partitions

– Cell structures (Theory A)– Projective relation to reality (Theory

B)

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Theory ACells and Subcells

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Species Genera as Tree

canary

animal

bird fish

ostrich

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Species-Genera as Map/Partition

animal

bird

canary

ostrich

fish

canary

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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)

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Theory BProjection of Cells onto Reality

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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

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Misprojection

…

Montana

Wyoming

…

P(‘Montana’,Montano) and L(Montana,’Montana’)

P(‘Wyoming’,Sicily) but not L(Sicily,’Wyoming’)

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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)

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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)

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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

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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

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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

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Preserve mereological structure

Helium

Noble gases

Neon

EmptyNeonHelium

gasesNobleNeon

gasesNobleHelium

EmptyNeHe

NGNe

NGHe

Potential of preserving mereological structure

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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.

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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

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Classification of granular partitions

according to

• Degree of preservation of mereological structure

• Degree of completeness of correspondence

• Degree of redundancy

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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

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Projective completeness

Empty cells

function totala is Projection

scompletnes Projective

),(:),( zoLoAzZ

Every cell has an objectlocated within it:

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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

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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