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From Formal Ontology to Biomedical Ontology

Barry Smith

http://ifomis.org

Biomereology

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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 early Tarski

late Carnap (geometry of solids)

Grzegorczyk

(mereotopology)

set-theory as mereology as

principal instrument principal instrument

of formal ontology of formal ontology

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Hilbert Leśniewski

late Tarski Russell

Carnap early Tarski

Putnam Woodger

contemporary contemporary

model-theoretic realist ontology

semantics

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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

tragicallyafter 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 Leśniewski

late Tarski Russell

Carnap Wittgenstein

Putnam Quine

OLD: Logic as

Language

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Hilbert Leśniewski

late Tarski Russell

Carnap Wittgenstein

Putnam Quine

NEW: Logic as

Calculus

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Hilbert Leśniewski late Tarski Russell Carnap Wittgenstein Putnam Quine

OLD: Set-theory- based-model-theoretic semantics... possible worlds

blah blah

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Hilbert Leśniewski

late Tarski Russell

Carnap early Tarski

Putnam 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 Categoriesobject

state of affairs

unity

plurality

boundary

dependent part

independent part

relation

are able to form complex structures in non-arbitrary, law-governed ways

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From Formal Ontology

to Biomedical Ontology

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Scales of anatomy

DNA

Protein

Organelle

Cell

Tissue

Organ

Organism

10-5 m

10-1 m

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 scientificcultures / terminologies

immunology

genetics

cell biology

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Fleck on Thought-Styles

the general structure of a thought-collective 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 textsWhat if sciences are identified with

information systems ?

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ProblemEach (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

GLUING THESE TOGETHER MEREOLOGICALLY YIELDS ONTOLOGICAL MONSTERS

processes

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Substances and processes exist in time in different ways

substance

t i m

e

process

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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 four-dimensional 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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DNA

Protein

Organelle

Cell

Tissue

Organ

Organism

10-5 m

10-1 m

Scales of anatomy

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

59what 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

Orange

VegetableSimilarTo

ApfelsineSynonymWith

NarrowerThan

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

67UMLS Semantic Network

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Vitamin

Injury or Poisoning

causes

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Bacterium

Experimental Model of Disease

causes

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Manufactured Object

Disease or Syndromecauses

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Biomedical or Dental Material

Mental or Behavioral

Dysfunctioncauses

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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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WoodgerThe Axiomatic Method in Biology

part_of

earlier_than

derives_by_division_or_fusion_from

environment_of

is_a_cell

is_a_male_gamete

is_a_female_gamete

is_a_whole_organism

is_an_organized_unity

is_a_genetic_property

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Material Primitives

part_of

earlier_than

derives_by_division_or_fusion_from

environment_of

is_a_cell

is_a_male_gamete

is_a_female_gamete

is_a_whole_organism

is_an_organized_unity

is_a_genetic_property

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Formal Primitives

part_of

earlier_than

derives_by_division_or_fusion_from

environment_of

is_a_cell

is_a_male_gamete

is_a_female_gamete

is_a_whole_organism

is_an_organized_unity

is_a_genetic_property

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Formal Primitives

part_of

earlier_than

derives_by_division_or_fusion_from

environment_of

is_a_cell

is_a_male_gamete

is_a_female_gamete

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_apart_ofdevelops_ fromderives_ from located_atparticipates_inadjacent_tocontained_inprecedeshas_function

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Woodger’s Formal Primitives

part_of

earlier_than

derives_by_division_or_fusion_from

environment_of

is_a_cell

is_a_male_gamete

is_a_female_gamete

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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Pleural Cavity

Pleural Cavity

Interlobar recess

Interlobar recess

Mesothelium of Pleura

Mesothelium of Pleura

Pleura(Wall of Sac)

Pleura(Wall of Sac)

VisceralPleura

VisceralPleura

Pleural SacPleural Sac

Parietal Pleura

Parietal Pleura

Anatomical SpaceAnatomical Space

OrganCavityOrganCavity

Serous SacCavity

Serous SacCavity

AnatomicalStructure

AnatomicalStructure

OrganOrgan

Serous SacSerous Sac

MediastinalPleura

MediastinalPleura

TissueTissue

Organ PartOrgan Part

Organ Subdivision

Organ Subdivision

Organ Component

Organ Component

Organ CavitySubdivision

Organ CavitySubdivision

Serous SacCavity

Subdivision

Serous SacCavity

Subdivision

88Pleural Cavity

Pleural Cavity

Pleura(Wall of Sac)

Pleura(Wall of Sac)

Pleural SacPleural Sac

Parietal Pleura

Parietal Pleura

Anatomical SpaceAnatomical Space

OrganCavityOrganCavity

Serous SacCavity

Serous SacCavity

AnatomicalStructure

AnatomicalStructure

OrganOrgan

Serous SacSerous Sac TissueTissue

Organ PartOrgan Part

Organ Subdivision

Organ Subdivision

Organ Component

Organ Component

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Pleural Cavity

Pleural Cavity

Interlobar recess

Interlobar recess

Mesothelium of Pleura

Mesothelium of Pleura

Pleura(Wall of Sac)

Pleura(Wall of Sac)

VisceralPleura

VisceralPleura

Pleural SacPleural Sac

Parietal Pleura

Parietal Pleura

Serous SacCavity

Serous SacCavity Serous SacSerous Sac

MediastinalPleura

MediastinalPleura

TissueTissueOrgan Subdivision

Organ Subdivision

Organ Component

Organ Component

Serous SacCavity

Subdivision

Serous SacCavity

Subdivision

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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

DNA

Protein

Organelle

Cell

Tissue

Organ

Organism

10-5 m

10-1 m

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