1. Introduction Functions and dispositions Conclusions
Relating functions and dispositions using
nonmonotonic reasoning
Robert Hoehndorf1,2 , Janet Kelso2 , Heinrich Herre1
1 Institute
for Informatics
and
Research Group Ontologies in Medicine, Institute for Medical Informatics,
Statistics and Epidemiology, University of Leipzig
2 Department of Evolutionary Genetics, Max-Planck-Institute for Evolutionary
Anthropology

2. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
Gene Ontology (molecule function)
Celltype Ontology (cell function)
FMA, Anatomie (organ function)
Disease Ontology, (Human/Mammalian) Phenotype Ontology
(malfunctioning)
OBI (device function)
Protein Ontology

3. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
A solved problem?
A function f is
1 a realizable dependent continuant, which
2 has a bearer which is an independent continuant, and
3 is of a type instances of which typically have realizations; each
realization is
1 a process in which the bearer is a participant,
2 that occurs in virtue of the bearer’s physical makeup,
3 this physical make-up is something which that bearer possesses
because of how it came into being.
Arp and Smith, 2008

4. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
BFO: The function of the heart is to make thumping noises
A function f is
a realizable dependent continuant, which
“To make thumping noises” is realizable.

5. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
BFO: The function of the heart is to make thumping noises
A function f is
a realizable dependent continuant, which
“To make thumping noises” is realizable.
has a bearer which is an independent continuant, and
The heart is an independent continuant.

6. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
BFO: The function of the heart is to make thumping noises
A function f is
a realizable dependent continuant, which
“To make thumping noises” is realizable.
has a bearer which is an independent continuant, and
The heart is an independent continuant.
is of a type instances of which typically have realizations;
“To make thumping noises” is typically realized.

7. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
BFO: The function of the heart is to make thumping noises
Each realization is
a process in which the bearer is a participant,
Hearts participate in thumping-noise-making processes.

8. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
BFO: The function of the heart is to make thumping noises
Each realization is
a process in which the bearer is a participant,
Hearts participate in thumping-noise-making processes.
that occurs in virtue of the bearer’s physical makeup,
Thumping-noise-making occurs due to the physical makeup of
the heart.

9. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
BFO: The function of the heart is to make thumping noises
Each realization is
a process in which the bearer is a participant,
Hearts participate in thumping-noise-making processes.
that occurs in virtue of the bearer’s physical makeup,
Thumping-noise-making occurs due to the physical makeup of
the heart.
this physical make-up is something which that bearer
possesses because of how it came into being.
Heart possess their makeup due to how they came into being.

10. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
BFO: The function of the heart is to make thumping noises
Each realization is
a process in which the bearer is a participant,
Hearts participate in thumping-noise-making processes.
that occurs in virtue of the bearer’s physical makeup,
Thumping-noise-making occurs due to the physical makeup of
the heart.
this physical make-up is something which that bearer
possesses because of how it came into being.
Heart possess their makeup due to how they came into being.
Therefore: The function of the heart is to make thumping noises.
(BFO)

11. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
Function in BFO
functions may “typically” not be realized: sperm cells
functions may be acquired after through transformation (not
at time of creation): angiotensin I to angiotensin II
what is a realization?

12. Introduction Functions and dispositions Conclusions
Functions in biomedical ontologies
Realizations
What makes a process a realization of a function?
Participation of the function bearer is not sufficient.
A protein’s function “to transport” is
realized by transport processes,
in which the protein participates
as a transporter.
Mode of participation in a process necessary to understand
realizations.
Use of processual or relational roles/qua entities

13. Introduction Functions and dispositions Conclusions
Ontology of Functions (OF)
Conceptual framework to
model functions
Implemented in OWL

14. Introduction Functions and dispositions Conclusions
Ontology of Functions (OF)
Open questions
What is the relation between function and disposition?
What is the relation between function and causality?
How do functions come into being?
What is a function?

15. Introduction Functions and dispositions Conclusions
Larry Wright
Reducing function to causality
The function of X is Z means
1 X is there because it does Z ,
2 Z is a consequence (or result) of X ’s being there.

16. Introduction Functions and dispositions Conclusions
John Searle
Functions as social concepts
All functions are socially ascribed by an agent to an object.
Functions are always observer-relative.
Function ascription is based on brute facts.

17. Introduction Functions and dispositions Conclusions
Nicolai Hartmann
Function ascription and causality
1 Setting a goal (in the future)
2 Planning the goal’s realization
3 Realizing the goal (causally)
(1) and (2) create functionality
Must realization be possible?

18. Introduction Functions and dispositions Conclusions
Malfunctionings
Overview
Setting a goal
Planning
No realization possible: missing disposition
Malfunctioning is function without disposition.
Functionality does not imply causality.
But: normally, function-bearers have the disposition to realize
their function.
Normally, entities do not malfunction.

19. Introduction Functions and dispositions Conclusions
Malfunctionings
Formal characterization
If e has the function f (with goal Tgoal ), and e is not
malfunctioning, then e has a disposition with goal Tgoal .
A(mf ) = hasFunction(e, f ) ∧ f :: F ∧ ¬mf (e) →
∃d(d :: D ∧ isa(D, Disposition) ∧ inheresIn(d, e)∧
Treq (F ) = Treq (D) ∧ Tgoal (F ) = Tgoal (D))

20. Introduction Functions and dispositions Conclusions
Malfunctionings
Formal characterization
If e has the function f (with goal Tgoal ), and e is not
malfunctioning, then e has a disposition with goal Tgoal .
A(mf ) = hasFunction(e, f ) ∧ f :: F ∧ ¬mf (e) →
∃d(d :: D ∧ isa(D, Disposition) ∧ inheresIn(d, e)∧
Treq (F ) = Treq (D) ∧ Tgoal (F ) = Tgoal (D))
Normally, e is not malfunctioning.
A(mf )∧∀P((A(P) ∧ ∀x(P(x) → mf (x))) →
(∀x(P(x) ↔ mf (x))))

21. Introduction Functions and dispositions Conclusions
Malfunctionings
Non-monotonicity
Classical (monotonic) inference:
S ⊆ T → S |= ⊆ T |=
non-monotonic inference permits default reasoning
e is not malfunctioning as long as not proven otherwise
use of default logics, circumscription or auto-epistemic logics
implementation using answer-set programming

22. Introduction Functions and dispositions Conclusions
Application
Functions and malfunctionings
Human (functional) anatomy: Ear CC-hasFunction Hearing
∀x(x :: Ear → ∃y (y :: Hearing ∧ II-hasFunction(x, y )))
Disposition D to participate in hearing processes (realization)
as receiver (role)
If an instance e of Ear is not malfunctioning, it has a
disposition d (which is an instance of D).
Normally, instances of Ear are not malfunctioning (with
respect to Hearing ).
Deafness (HP:0000404) implies malfunctioning of its bearer
w.r.t. Hearing

23. Introduction Functions and dispositions Conclusions
Summary
BFO’s definition of function needs refinement.
Philosophical explanations of biological functions can be
divided in:
reductions to causality
social ascription
each relates functionality to causality
most use normality or typicality
non-monotonic reasoning is necessary to formalize normality
focus on necessary conditions and inferences instead of
definitions for function

24. Introduction Functions and dispositions Conclusions
Acknowledgements
Heinrich Herre
Janet Kelso
Patryk Burek
Frank Loebe
Hannes Michalek

25. Introduction Functions and dispositions Conclusions
Thank you!

26. Introduction Functions and dispositions Conclusions
Dispositions
An individual e has the disposition d to cause an instance of Tgoal
iff e causes a situation s :: Tgoal whenever e is placed in the right
circumstances.
Describe “in the right circumstances” using a
situational/relational role.
Dispositions are possibilities to cause certain states of affairs
to become factual.
What is the relation between function and disposition?