From Knowledge Representation to Reality Representation

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From Knowledge Representation to Reality
Representation

• Barry Smith

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2002

• Institute for Formal Ontology and Medical
  Information Science (Germany)
• initially work on formal ontology
• and on ontology-based quality control in medical
  terminologies
• (UMLS, SNOMED, NCI Thesaurus, etc.)

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Problem Associative approach to word meanings
SimilarTo
Fruit
Vegetable
NarrowerThan
Orange
Apfelsine
SynonymWith
Goble Shadbolt
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• both testes is_a testis
• plant leaves is_a plant
• menopause part_of death
• bacterium causes experimental model of disease
• not normal cell is_a cell
• not abnormal cell is_a cell

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move from associative relations between meanings
to ontological relations between the entities
themselves

• supplementing data mining approaches with
• better data
• better annotations
• better integration
• the possibility of strong logical reasoning

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First crack in the wall

• Digital Anatomist Foundational Model of
  Anatomy(Department of Biological Structure,
  University of Washington, Seattle)
• Virtual Soldier Project
• Reference Ontology of Anatomy
• Reference Ontology of Physiology
• Reference Ontology of Disease Pathways

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Second Crack in the Wall

• Gene Ontology Consortium
• Open Biological Ontologies

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NCOR National Center for Ontological Research

• Buffalo Center of Excellence in Bioinformatics)
• Stanford Medical Informatics (Protégé 2000)
• Berkeley Drosophila Genome Project
• (Model Organism Phenotype Ontology Project)

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NCOR National Center for Ontological Research

• plus industrial parners
• Ontology Works
• ...

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NCOR Methodology

• work with content developers to ensure rigorous
  conformity with good principles of classification
  and definition
• use formally defined categories and relations to
  ensure interoperability and support automatic
  reasoning
• and to move beyond mere statistical / associative
  techniques

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Goal in Biomedical Informatics

• use the methodology of formally defined
  relations and a common top-level ontology to
  bridge the granularity gap between genomics and
  proteomics data and phenotype (clinical,
  pharmacological, patient centered) data
• From molecules to diseases

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Examples of simple formal-ontological structures

• is_a hierarchies
• part_of hierarchies
• dependence relations

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A Window on Reality
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Medical Diagnostic Hierarchy
a hierarchy in the realm of diseases
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Dependence Relations
Organisms
Diseases
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A Window on Reality
Organisms
Diseases
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Anatomical Space
Anatomical Structure
Organ Cavity Subdivision
Organ Cavity
Organ
is_a
Serous Sac
Organ Component
Serous Sac Cavity
Tissue
Serous Sac Cavity Subdivision
Pleural Sac
Pleura(Wall of Sac)
Pleural Cavity
part_of
Parietal Pleura
Visceral Pleura
Interlobar recess
Mediastinal Pleura
Mesothelium of Pleura
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A Window on Reality
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We can reason across such hierarchies and
combinations

• but only if the top-level categories and
  associated formal-ontological relations are
  well-defined and used consistently

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Formal-Ontological Categories

object process site layer fragment quality function relation boundary region
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Formal-Ontological Relations
is_identical_to is_a part_of develops_ from derives_ from located_at depends_on is_boundary_of has_participant has_agent adjacent_to contained_in precedes is_functioning_of has_function intends
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To support integration of ontologies

• relational expressions such as
• is_a
• part_of
• ...
• should be used in the same way by all the
  ontologies to be integrated
• NCOR goal

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to define these relations properly

• we need to take account of reality
• If we remain in the realm of concepts we will
  forever face problems of interoperability

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to define these relations properly

• we need to take account not of concepts,
• but of universals and instances in reality

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Tom Gruber

• An ontology is a specification of a
  conceptualization

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The Concept Orientation

• Work on biomedical ontologies grew out of work on
  medical dictionaries and thesauri
• led to the assumption that all that need be said
  about concepts can be said without appeal to time
  or instances.
• fostered an impoverished regime of definitions

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Concept in ontology runs together

1. the meaning that is shared in common by a
   collection of synonymous terms
2. an idea shared in common in the minds of those
   who use synonymous terms (psycho-linguistic view)
3. a universal, feature or property shared by
   entities in the world which fall under the concept

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Problem of evaluation

• if an ontology is a mere specification of a
  conceptualization, then the distinction between
  good and bad ontologies loses its foothold in
  reality

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There are more word meanings than there are types
of entities in reality

• unicorn
• devil
• cancelled performance
• avoided meeting
• prevented pregnancy
• imagined mammal ...

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• A is_a B def.
• A is more specific in meaning than B

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• unicorn is_a one-horned mammal
• alien implant removal is_a surgical process
• Chios energy healing is_a therapeutic process

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This linguistic reading

• yields a more or less coherent reading of
  relations like
• is_a
• synonymous_with
• associated_to

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but it fails miserably when it comes to relations
of other types

• part_of def. composes, with one or more other
  physical units, some larger whole
• contains def. is the receptacle for fluids or
  other substances.

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for how can concepts, on the linguistic reading,
figure as relata of relations like

• part_of
• adjacent_to
• connected_to

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connected_to def. Directly attached to another
physical unit as tendons are connected to
muscles.

• How can a meaning or concept be directly
  attached to another physical unit as tendons are
  connected to muscles ?

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is_a

• human is_a mammal
• all instances of the universal human are as a
  matter of necessity instances of the universal
  mammal

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Evaluation

• Good ontologies are those whose general terms
  correspond to universals in reality, and thereby
  also to corresponding instances.

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Kinds of relations

• ltuniversal, universalgt is_a, part_of, ...
• ltinstance, universalgt this explosion instance_of
  the universal explosion
• ltinstance, instancegt Marys heart part_of Mary

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Instance-level relations

• part_of
• is_located_at
• has_participant
• has_agent
• earlier
• . . .

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• part_of
• For instances
• part_of instance-level parthood
• (for example between Mary and her heart)
• For universals
• A part_of B def. given any instance a of A there
  is some instance b of B such that a part_of b

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transformation_of
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transformation_of

• fetus transformation_of embryo
• adult transformation_of child
• C2 transformation_of C1 def. any instance of C2
  was at some earlier time an instance of C1

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derives_from

• c derives_from c1
• def c and c1 are non-identical
• and exist in continuous succession

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the initial component ceases to exist with the
formation of the new component
C c at t
C1 c1 at t1
the new component detaches itself from the
initial component, which itself continues to exist
C c at t
c at t1
C1 c1 at t
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two initial components fuse to form a new
component
C1 c1 at t1
C c at t
C' c' at t
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Functions

• your heart has the function to pump blood
• your heart is predisposed (has the potential or
  casual power) to realize a process of the type
  pumping blood.
• has_agent (instance-level relation)
• p is_functioning_of c ? p has_agent c

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Example Spatially Coinciding Objects with
thanks to Maureen Donnelly
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Two entities coincide (partially) when they
overlap (share parts)

• my hand coincides with my body
• the European Union coincides with the British
  Commonwealth
• (United Kingdom Malta, Cyprus)

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Some entities coincide even though they share no
parts

• any material object coincides with its spatial
  region
• a portion of food coincides with my stomach cavity

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Holes may coincide with material objects

• The hole in the chunk of amber coincides
  completely with, but does not overlap, the
  encapsulated insect which fills it
• Sometimes holes and objects are moving
  independently (a bullet flying through a railway
  carriage moving through a tunnel)

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Layers
co-located objects
The region layer
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Layered Ontology of Lakes

• L1. a region layer
• L2. a lake layer, consisting of a certain
  concave portion of the earths surface together
  with a body of water
• L3. a fish layer
• L4. a chemical contaminant layer

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Layered Epidemiology Ontology

• L1. a two-dimensional region layer in some
  undisclosed location
• L2. a topographical layer, consisting of
  mountains, valleys, deserts, gullies
• L3. a storm-system occupying sub-regions of L2
• L4 an airborne cloud of smallpox virus particles.

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Layered Mereology

• modified General Extensional Mereology (GEM)

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Parthood (P)

• Parthood is a partial ordering
• (P1) Pxx (reflexive)
• (P2) Pxy Pyx -gt x y (antisymmetric)
• (P3) Pxy Pyz -gt Pxz (transitive)
• (P4) Pxy -gt z(Pzx Ozy)
• (the remainder principle if x is not part of y,
  then x has a part that does not overlap y)

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co-located objects
The region layer
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The Region Function

• r(x) the region at which x is exactly located.
• r is a new primitive
• r maps (collapses) entities on all higher layers
  onto the region layer

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Axioms for the region function, e.g.

• (R3) Pxy ? P r(x)r(y)

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Some Theorems

• Ry ? r(y) y
• (every region is located at itself)
• (?x? ?x(? ? Rx)
• "y (Oyz lt-gt x (f Oyx))) ? Rz
• (every sum of regions is a region)

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Defined Relations

• ECxy Cxy Oxy
  
• (x and y are externally connected)
• Axy EC(r(x), r(y))
• (x and y abut)

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Towards Dynamic Spatial OntologyFrom spatial
coincidence to spatio-temporal coincidence
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Objects move through space

• An adequate ontology of motion requires at least
  two independent sorts of spatial entities
• 1. locations, which remain fixed,
• 2. objects, which move relative to them.

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Standard (RCC) approaches

• sparrow 152 moves from one location (region A)
  to another (region B)
• Becomes
• each member of this continuous sequence of
  sparrow-shaped regions, starting with A and
  ending with B, has at successive times,
  rufous-winged (etc.) attributes.
• Instead of talking about sparrows flying through
  the sky, we talk of mappings of the form
• Sparrow152 time ? regular closed subsets of R3.

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Region-based approaches (RCC, etc.)

• have no means of distinguishing true overlap
  (i.e. the sharing of parts) from mere spatial
  co-location.
• They identify the relation of a fish to the lake
  it inhabits with the relation of a genuine part
  of a lake (a bay, an inlet) to the lake as a
  whole.
• They identify the genuine parts of the human
  body, such as the heart or lungs, with foreign
  occupants such as parasites or shrapnel.

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The solution

• is to recognize both objects and locations, on
  separate layers
• and then we need a theory of coincidence and of
  layered mereotopology to do justice to the
  entities in these two categories

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Some entities coincide spatially even though they
share no parts

• a portion of food coincides with my stomach
  cavity at a certain time

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Some entities coincide spatio-temporally even
though they share no parts

• the course of a disease coincides with the
  treatment of the disease

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Processes may coincide with each other

• The manouvres of the coalition troops coincide,
  but do not share parts in common, with the
  activities of the terrorists

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Spatiotemporal Coincidence without Sharing of
Parts

• The Great Plague of 1664 coincides with, but does
  not overlap, the history of Holland in the 17th
  century
• A process of deforestation coincides with, but
  does not overlap, the history of the forest

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Objects and processes do not coincide

• For they are of different dimension
• Objects are 3-dimensional
• Processes are 4-dimensional
• Object-layers are always 3-dimensional
• Process-layers are always 4-dimensional

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Two ontologies of motion and change

• series of samples, or snapshots
• object x1 is at region r1 at time t1
• object x2 is at region r2 at time t2
• object x3 is at region r3 at time t3
• ? SNAP ontologies (ontologies indexed by times)

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t1
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t2
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t3
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SNAP vs SPAN

• Continuants vs Occurrents
• (Sampling vs. Tracking)

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SPAN ontology
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SPAN ontology

• is an ontology which recognizes processes,
  changes, themselves
• four-dimensional (spatio-temporal) entities
• not via a sequence of instantaneous samplings but
  via extended observations

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Many different interconnections traverse the
SNAP-SPAN divide

• But SNAP and SPAN entities are never related by
  part_of, connected_to or coincidence (layer)
  relations

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SNAP
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SPAN
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There are layers in both the SNAP (object)
ontology and the SPAN (process) ontology

• In SNAP the region layer space
• In SPAN the region layer spacetime

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But

• distinguishing layers in the process realm of
  SPAN is a matter of gerrymandering (of fiat
  carvings) to a much greater degree than in the
  realm of SNAP

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One big difference between SNAP and SPAN

• In SNAP, higher layers are categorially
  well-distinguished nicely separated (physical
  objects, holes, administrative entities )
• In SPAN

everything is flux
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