Introduction Functions and dispositions Conclusions

Relating functions and dispositions usingnonmonotonic reasoning

Robert Hoehndorf1,2, Janet Kelso2, Heinrich Herre1

1Institute for Informaticsand

Research Group Ontologies in Medicine, Institute for Medical Informatics,Statistics and Epidemiology, University of Leipzig

2Department of Evolutionary Genetics, Max-Planck-Institute for EvolutionaryAnthropology

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

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesA solved problem?

A function f is

1 a realizable dependent continuant, which

2 has a bearer which is an independent continuant, and3 is of a type instances of which typically have realizations; each

realization is1 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

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesBFO: 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.

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesBFO: 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.

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesBFO: 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.

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesBFO: 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 ofthe heart.

this physical make-up is something which that bearerpossesses 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)

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesBFO: 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 ofthe heart.

this physical make-up is something which that bearerpossesses 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)

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesBFO: 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 ofthe heart.

this physical make-up is something which that bearerpossesses 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)

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesBFO: 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 ofthe heart.

this physical make-up is something which that bearerpossesses 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)

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesFunction in BFO

functions may “typically” not be realized: sperm cells

functions may be acquired after through transformation (notat time of creation): angiotensin I to angiotensin II

what is a realization?

Introduction Functions and dispositions Conclusions

Functions in biomedical ontologiesRealizations

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 participatesas a transporter.

Mode of participation in a process necessary to understandrealizations.

Use of processual or relational roles/qua entities

Introduction Functions and dispositions Conclusions

Ontology of Functions (OF)

Conceptual framework tomodel functions

Implemented in OWL

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?

Introduction Functions and dispositions Conclusions

Larry WrightReducing 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.

Introduction Functions and dispositions Conclusions

John SearleFunctions 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.

Introduction Functions and dispositions Conclusions

Nicolai HartmannFunction 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?

Introduction Functions and dispositions Conclusions

MalfunctioningsOverview

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 realizetheir function.

Normally, entities do not malfunction.

Introduction Functions and dispositions Conclusions

MalfunctioningsFormal characterization

If e has the function f (with goal Tgoal), and e is notmalfunctioning, 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))))

Introduction Functions and dispositions Conclusions

MalfunctioningsFormal characterization

If e has the function f (with goal Tgoal), and e is notmalfunctioning, 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))))

Introduction Functions and dispositions Conclusions

MalfunctioningsNon-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

Introduction Functions and dispositions Conclusions

ApplicationFunctions 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 adisposition d (which is an instance of D).

Normally, instances of Ear are not malfunctioning (withrespect to Hearing).

Deafness (HP:0000404) implies malfunctioning of its bearerw.r.t. Hearing

Introduction Functions and dispositions Conclusions

Summary

BFO’s definition of function needs refinement.

Philosophical explanations of biological functions can bedivided in:

reductions to causalitysocial 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 ofdefinitions for function

Introduction Functions and dispositions Conclusions

Acknowledgements

Heinrich Herre

Janet Kelso

Patryk Burek

Frank Loebe

Hannes Michalek

Introduction Functions and dispositions Conclusions

Thank you!

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 rightcircumstances.

Describe “in the right circumstances” using asituational/relational role.

Dispositions are possibilities to cause certain states of affairsto become factual.

What is the relation between function and disposition?