Biomereology
From Formal Ontology to
Biomedical Ontology
Barry Smith
http://ifomis.org
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Mereology as Formal Ontology
Logical Investigations (1900-01)
Investigation III:
On the Theory of Wholes and Parts
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Husserl
Leśniewski
Kotarbiński
Tarski
Grzegorczyk
Woodger
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Cantor
Leśniewski
Frege
late Carnap
early Tarski
(geometry of solids)
Grzegorczyk
(mereotopology)
set-theory as
principal instrument
of formal ontology
mereology as
principal instrument
of formal ontology
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Hilbert
late Tarski
Carnap
Putnam
contemporary
model-theoretic
semantics
Leśniewski
Russell
early Tarski
Woodger
contemporary
realist ontology
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For Frege, Russell, Leśniewski,
Wittgenstein, Quine …
logic is a zoology of facts
formal theories are theories of reality
with one intended interpretation: the world
tragically
after starting off on the right road
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Logic took a wrong turn
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(Tarski)
Carnap, Putnam, Goodman, etc.:
Forget reality!
Lose yourself in ‘models’!
“internal realism” ...
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Hilbert
late Tarski
Carnap
Putnam
Leśniewski
Russell
Wittgenstein
Quine
OLD: Logic as
Language
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Hilbert
late Tarski
Carnap
Putnam
Leśniewski
Russell
Wittgenstein
Quine
NEW: Logic as
Calculus
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Hilbert
late Tarski
Carnap
Putnam
Leśniewski
Russell
Wittgenstein
Quine
OLD: Set-theorybased-modeltheoretic semantics
... possible worlds
blah blah
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Hilbert
late Tarski
Carnap
Putnam
Leśniewski
Russell
early Tarski
Woodger
NEW: Extreme
Mereotopological
Bio-Ontological Realism
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Husserl + Leśniewski
realist mereology-based ontology
+ universals
+ topology
+ relations
+ dependent entities
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Formal Ontology vs. Formal Logic
Formal ontology deals with formal
ontological structures
Formal logic deals with formal logical
structures
‘formal’ = domain-neutral
(obtain in all material spheres of reality)
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Formal Ontology
the theory of those ontological structures
(such as part-whole, universal-particular)
which apply to all domains whatsoever
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Formal Ontology vs. Formal Logic
Formal ontology deals with the
interconnections of things
with objects and properties, parts and
wholes, relations and collectives
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Formal-Ontological Categories
object
state of affairs
unity
plurality
boundary
dependent part
independent part
relation
are able to form complex structures in nonarbitrary, law-governed ways
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From Formal Ontology
to Biomedical Ontology
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Scales of anatomy
Organism
Organ
10-1 m
Tissue
Cell
10-5 m
Organelle
Protein
DNA
10-9 m
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Complexity of biological structures
30,000 genes in human
200,000 proteins
100s of cell types
100,000s of disease types
1,000,000s of biochemical pathways
(including disease pathways)
A new golden age of classification
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A new golden age of classification
central importance of classes /
types / kinds / universals / species
of independent objects
dependent objects
processes
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Different scientific
cultures / terminologies
immunology
genetics
cell biology
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Fleck on Thought-Styles
the general structure of a thoughtcollective entails that the communication
of thoughts within the collective,
irrespective of content or logical
justification, leads for sociological reasons
to the reinforcement of the thought
structure
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The problem of the unity of science
The logical positivist solution to this
problem addressed a world in which
sciences are identified with
printed texts
What if sciences are identified with
information systems ?
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Problem
Each (clinical, pathological, genetic,
proteomic, pharmacological …) information
system uses its own classification system
How can we overcome the incompatibilities
which become apparent when data from
distinct sources needs to be combined?
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Solution:
“Ontology”
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Compare:
1) pure mathematics (theories of structures
such as order, set, function, mapping)
employed in every domain
2) applied mathematics, applications of
these theories = re-using the same
definitions, theorems, proofs in new
application domains
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Three levels of ontology
1) formal ontology (mereology,
mereotopology, …)
2) domain ontologies
= Foundational Model of Anatomy, Gene
Ontology, Unified Medical Language
System, SNOMED
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Biomereology must be rich
enough to deal with time and
change
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Leśniewski’s mereology
grew out of his concerns with the
foundations of mathematics
LIKE SET THEORY, IT DOES NOT TAKE
ACCOUNT OF TIME
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The Problem
The tumor developed in John’s lung over
25 years
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The Problem
____ developed in _____ over 25 years
process
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The Problem
The tumor developed in the lung over 25 years
substances
things
objects
continuants
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The Problem
The tumor developed in the lung over 25 years
WHAT IS PART OF WHAT
IS NOT DETERMINATE
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The Problem
The tumor developed in the lung over 25 years
substances
processes
GLUING THESE TOGETHER
MEREOLOGICALLY YIELDS ONTOLOGICAL
MONSTERS
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Substances and processes
exist in time in different ways
process
substance
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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
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Fourdimensionalism
– only processes exist
– time is just another dimension, analogous
to the three spatial dimensions
– substances are analyzed away as
worms/fibers within the four-dimensional
plenum
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There are no substances
Bill Clinton does not exist
Rather: there exists within the fourdimensional plenum a continuous
succession of processes which are
similar in a Billclintonizing sort of way
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Fourdimensionalism solves the
problems of
universal applicability of mereology
indeterminacy of parthood
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Fourdimensionalism (the SPAN
perspective) is right in
everything it says
But incomplete
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The response to anyone who
believes that fourdimensionalism is
the whole truth about reality is:
see a doctor
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The response to anyone who
believes that fourdimensionalism is
the whole truth about reality is:
see any
organism
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Bio-Ontology requires two
orthogonal applications of
mereology
A fourdimensional ontology
supplemented by a
threedimensional ontology of
continuant entities
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How can a threedimensional
ontology solve the problem of
determinacy of parthood
PARTHOOD AT AN INSTANT IS
DETERMINATE
take an assay of what exists in the
three spatial dimensions always at
some specific instant of time
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The 4D and 3D ontologies represent
two complementary views
of the same rich and
messy reality
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Scales of anatomy
Organism
Organ
10-1 m
Tissue
Cell
10-5 m
Organelle
Protein
DNA
10-9 m
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A new golden age of classification
central importance of classes / types / kinds
/ universals / species
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and of is-a hierarchies
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cars
Cadillacs
blue cars
blue Cadillacs
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Confusions about ‘is-a’ and ‘part-of’
in bio-ontologies
Unified Medical Language System
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The UMLS Semantic
Network
a US Federal Government ontology
designed to unify all biomedical
terminologies
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what are the nodes in this graph?
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linguistic entities
≈ meanings
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UMLS SN
is_a =def.
if one item ‘is_a’ another item then
the first item is more specific in
meaning than the second item
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Fruit
SimilarTo
Vegetable
NarrowerThan
Orange
SynonymWith
Apfelsine
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Goble & Shadbolt
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How can concepts/meanings figure
as relata of relations such as
disrupts or contained in?
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Swimming is healthy and
contains 8 letters
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UMLS Semantic Network
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Injury or
Poisoning
Vitamin
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Experimental
Model of Disease
Bacterium
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Disease or
Syndrome
Manufactured
Object
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Mental or
Behavioral
Dysfunction
Biomedical or
Dental Material
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The Gene Ontology
a ‘controlled vocabulary’
designed to standardize annotation of
genes and gene products
used by over 20 genome database and
many other groups in academia and
industry
and methodology much imitated
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A part_of B =def A can be part of B
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The Gene Ontology
menopause part_of death
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GO: ‘within’
lytic vacuole within a protein storage vacuole
is-a protein storage vacuole
interval within a football match is-a football
match
embryo within a uterus is-a uterus
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GO: ‘extrinsic to’
extrinsic to membrane part-of membrane
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these people need our help
formal-ontological help
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Woodger
The Axiomatic Method in Biology
part_of
is_a_cell
earlier_than
is_a_male_gamete
derives_by_division_or
_fusion_from
is_a_female_gamete
environment_of
is_a_whole_organism
is_an_organized_unity
is_a_genetic_property
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Material Primitives
part_of
is_a_cell
earlier_than
is_a_male_gamete
derives_by_division_or
_fusion_from
is_a_female_gamete
environment_of
is_a_whole_organism
is_an_organized_unity
is_a_genetic_property
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Formal Primitives
part_of
is_a_cell
earlier_than
is_a_male_gamete
derives_by_division_or
_fusion_from
is_a_female_gamete
environment_of
is_a_whole_organism
is_an_organized_unity
is_a_genetic_property
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Formal Primitives
part_of
is_a_cell
earlier_than
is_a_male_gamete
derives_by_division_or
_fusion_from
is_a_female_gamete
environment_of
is_a_whole_organism
is_an_organized_unity
is_a_genetic_property
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Open Biological Ontologies
Consortium
http://obo.sourceforge.net/
OBO library of controlled vocabularies
developed for shared use across
different biological domains.
Gene Ontology plus: Cell Ontology,
Sequence Ontology, etc.
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Open Biological Ontologies
Consortium
European Bioinformatics Institute,
Cambridge
Jackson Labs, Bar Harbor, Maine
Berkeley Genetics,
Edinburgh Mouse Atlas Project
IFOMIS, Saarbrücken
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OBO Relations Ontology:
is_a
part_of
develops_ from
derives_ from
located_at
participates_in
adjacent_to
contained_in
precedes
has_function
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Woodger’s Formal Primitives
part_of
is_a_cell
earlier_than
is_a_male_gamete
derives_by_division_or
_fusion_from
is_a_female_gamete
environment_of
is_a_whole_organism
is_an_organized_unity
is_a_genetic_property
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Foundational Model of Anatomy
Reference Ontology
a graph-theoretical structure involving two
sorts of links or edges:
is-a (= is a subtype of )
(auditory ossicle is-a bone)
part-of
(cervical vertebra part-of vertebral column)
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Anatomical
Structure
Anatomical Space
Organ Cavity
Subdivision
Organ
Cavity
Organ
Serous Sac
Cavity
Subdivision
Serous Sac
Cavity
Serous Sac
Organ
Component
Organ
Subdivision
Pleural Sac
Pleural
Cavity
Parietal
Pleura
Interlobar
recess
Organ Part
Mediastinal
Pleura
Tissue
Pleura(Wall
of Sac)
Visceral
Pleura
Mesothelium
of Pleura
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Anatomical
Structure
Organ
Cavity
Serous Sac
Cavity
Organ
Organ Part
Serous Sac
Organ
Component
Pleural Sac
Pleural
Cavity
Organ
Subdivision
Tissue
Pleura(Wall
of Sac)
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Sac
ty
sion
Serous Sac
Cavity
Serous Sac
Organ
Component
Pleural Sac
Pleural
Cavity
Organ
Subdivision
Tissue
Pleura(Wall
of Sac)
Parietal
Pleura
Visceral
Pleura
Interlobar
recess
Mediastinal
Pleura
Mesothelium
of Pleura
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The Anatomy Reference Ontology
a coherent theory of part-of as a relation
between classes / types must be based on a
(mereological) theory of part-of as a relation
between instances
Mary’s heart part-of Mary
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Taking the instance-level part_of
as primitive
we can define:
A part_of B = any instance of A is part_of
some instance of B
nucleus part_of cell
but not:
testis part_of human
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from A part_of B we cannot infer that B
has_part A
human_testis part_of human
but not
human has_part human testis
running has_part breathing
but not
breathing part_of running
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Scales of anatomy
Organism
Organ
10-1 m
Tissue
Cell
10-5 m
Organelle
Protein
DNA
10-9 m
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Institute for Formal Ontology and
Medical Information Science
http://ifomis.org
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Buffalo Center for Ontological
Research
Two tenure-track faculty positions in
ontology
http://ontology.buffalo.edu/bcor
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The End
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