some issues in granularity daniel d. novotný ifomis workshop in freiburg, institute of medical...

Some Issues in

Granularity Daniel D. NovotnýIFOMIS

Workshop in Freiburg, Institute of Medical Informatics

January 22, 2005

Granularity in general:• many true perspectives on one reality

(Smith, Bittner)

Granularity in biomedicine: • is there a good set of such perspectives

spaning from molecules till organisms?• is it usefull to represent gran. levels in

biomedical ontologies?

DNA

Protein

Organelle

Cell

Tissue

Organ

Organism

10-5 m

10-1 m

10-9 m

Some candidates for the status of a

granularity level

adopted from Barry Smith

Overview

I. Accepted PrinciplesII. Controversial Principles:

A. Self-connectedness of GrainsB. Higher-order Granular Systems: Minimalism vs. Maximalism

III. A Note on FMA

Left Out: (a) Formalization, (b) Granularity in Physiology, (c) Tissues not a level

I. Accepted PrinciplesThese principles attempt to capture our intuitions and they involve therefore (at

this stage) some vagueness.

Principle 1 P1: Each level of granularity is determined by one class

or type of grain.


or type of grain.

Organs:


or type of grain.

Organs:

Cells:

Principle 2

P2: The grains in a given level are parts of the grains in the next higher level.

Principle 3

P3: Every level of granularity is such that summing all the grains together yields the

entire human body.

Principle 6

P6: With each level of granularity there is associated some specific type of causal

understanding.

Principle 8

P8: Grains have some parts at the same level of granularity.

(In other words: there is parthood across and within granularities).

Principle 8

If we rejected P8 and insisted on this rule:

If X is a part of Y, then X is not in the granular level of Y.

… we would have a granularity-level explosion.

Does parthood constitute granularity?

Face is a part of head, left eye is a part of face.

ERGO,

Face, left eye, head are in three levels of granularity?

Principle 8

Shall we accept this rule?

If X is a part of Y, then X is not in the granular level of Y.

No.

II. Controversial Principles

A. Self-connectedness of Grains

Self-Connectedness

A grain is a maximally self-connected entity with respect to some condition .

DEF: x is self-connected iff two parts of x are connected to each other.

DEF: x is -maximally self-connected iff (i) x satisfies (ii) x is self-connected, (iii) every y that satisfies and is self-connected is either disjoint from x or included in x.

Self-Connectedness

The crucial for defining grain of some level is to identify non-formal (presumably complex) property .

Possible candidates for include: • being generated by the coordinated expression

of the organism’s own genes (for Organism),• being made up of the same type of tissues (for

Organ), • being the minimal “independent” living unit (for

Cell), etc.

Self-Connectedness

Unfortunately, for instance, the endocrine system is disconnected.

Self-Connectedness

Possible Ways Out:

1. Give up Organ Systems as a Level of Granularity on its own

2. Give up Endocrine System as a Grain at the Level of Organ Systems

3. Give up the Principle of Self-Connectedness

Self-Connectedness

Possible Ways Out:




Novotny

Self-Connectedness

Possible Ways Out:




Novotny

Kumar, Smith

II. Controversial Principles

C. Higher-order Granular Systems

Higher-order Granular Systems

Is every entity at a given level of granularity either a grain or a (same level) granular-

part?


KUMAR’s and SMITH’s VIEW:

At a given level of granularity every entity is either a grain or a granular-part.


MY VIEW:

We should acknowledge Higher-Order Granular-Systems [GS]

GS are entities made up from grains at a given level of granularity – without

reaching the next higher level.


The two views have consequences:

My view is minimalist which means that I have as few granular-levels as possible with as much included in them as can be

"seen" in one perspective.


The two views have consequences:

Kumar’s and Smith’s view is maximalist which means that they have as many

granular-levels as possible.

KUMAR SMITH NOVOTNY

1. Organism 1. Organism 1. Organism

2. Organ System 2. Organ System

3. Cardinal Body Part ???

4. Organ 3. Organ 2. Organ

5. Organ Part 4. Organ Part

6. Tissue

7. Tissue Subdivision

8. Collect. of Cells ???

9. Cell 5. Cell 3. Cell

10. Collect. of organelle ???

11. Organelle 6. Organelle 4. Organelle

12. Biol. Macromol. 7. Biol. Macrom. 5. Biol. Macrom.

KUMAR SMITH NOVOTNY

1. Organism 1. Organism 1. Organism

2. Organ System 2. Organ System

3. Cardinal Body Part

4. Organ 3. Organ 2. Organ

5. Organ Part 4. Organ Part

6. Tissue

7. Tissue Subdivision

8. Collect. of Cells

9. Cell 5. Cell 3. Cell

10. Collect. of organelle

11. Organelle 6. Organelle 4. Organelle

12. Biol. Macromol. 7. Biol. Macrom. 5. Biol. Macrom.

NOVOTNY

1. Organism

2. Organ

3. Cell

4. Organelle

5. Biol. Macrom.

Granular-part

Grain Granular-system

Organism Level Body part Organism Taxon

Organ Level Organ Part

Organ Body Systems

Cell Level Cell part Cell Tissue

Subcell. Level Organelle part

Organnelle Coll. of Organnel.

Mollecule Level Atoms Biological Molecule

Coll. of Biol. Mol.

Minimalism vs. Maximalism

Advantages of minimalism:

(1) To identify levels of granularity is not difficult: Organism, Organ, Cell, Subcellular, Molecule Levels.

(2) We get rid of badly-behaving levels. (3) Authority: FMA claims that all entities (higher

than the Subcellular) are either (a) organs or cells,or (b) parts of organs or cells, or (c) constituted by organs or cells.




(2) We get rid of badly-behaving levels - such as Body System or Tissue. (Since granular-systems are not grains, they may violate principles for grains).




(2) We get rid of badly-behaving levels. (3) Authority: FMA claims that all entities (higher

than the Subcellular) are either (a) organs or cells, or (b) parts of organs or cells, or (c) constituted by organs or cells.


Advantages of maximalism:

(1) The formal framework might be less complicated than the framework for minimalism.

(2) Barry likes it.

DNA

Protein

Organelle

Cell

Tissue

Organ

Organism

10-5 m

10-1 m

10-9 m

Some candidates for the status of a

granularity level


Molecule

Organelle

Cell

Organ

Organism

10-5 m

10-1 m

10-9 m

Good candidates for the status of a

granularity level


IV. A Note on FMA

FMA - Foundational Model of Anatomy

Granularity:

FMA’s Metaknowledge explicitly states that every entity of Anatomical structure, except for

two (Acellular anatomical structure, Biological macromolecule), is either a cell or an organ or it is derived from them by being either

their part or constituted by them.

THIS VIEW CORRESPONDS TO THE MINIMALIST THEORY OF

GRANULARITY


Granularity:

However,


Granularity:

However,

The principle seems to be implemented only implicitly. One cannot see it, except in

definitions and by noticing some gaps…


Granularity:FMA’s partonomy for Brain:

– Brain+ Forebrain– Midbrain – Midbrain tectum

– Superior colliculus ° Zonal layer of superior colliculus ° Superficial gray layer of superior colliculus ° Superficial white layer of superior colliculus ° Stratum lemnisci of superior colliculus ° Middle gray layer of superior colliculus.....




– Superior colliculus ° Zonal layer of superior colliculus ° Superficial gray layer of superior colliculus ° Superficial white layer of superior colliculus ° Stratum lemnisci of superior colliculus ° Middle gray layer of superior colliculus.....

Middle gray layer of superior collicus is the smallest part of brain!




– Superior colliculus ° Zonal layer of superior colliculus ° Superficial gray layer of superior colliculus ° Superficial gray layer of superior colliculus ° Stratum lemnisci of superior colliculus ° Middle gray layer of superior colliculus.....

There is, of course, an implicit condition:

Middle gray layer of superior collicus is the smallest part of brain within the same level of

granularity (Organ).




– Superior colliculus ° Zonal layer of superior colliculus ° Superficial gray layer of superior colliculus ° Superficial gray layer of superior colliculus ° Stratum lemnisci of superior colliculus ° Middle gray layer of superior colliculus.....

This condition, however, should be made explicit.

Within FMA/Protégé this could be easily done by adding a slot with a value for the level of granularity and indicating whether a given entity is a

grain. (Whether it is a granular-part or

granular-system could be then determined automatically)

Further Work

Other topics for a discussion: (a) formalization, (b) granularity in physiology.

• Implement minimalism/ maximalism and test them;

• Philosophical Issues: Integral Wholes and “Lesser” Integral Wholes (traditional problems of unum and of individuum)

• Fiat or bona fide levels?Foto: Vojtěch Vlk

III. Formalization

A. Minimalism

Formalization of the Maximalist Approach

PRIMITIVES

UN(x) being a universal

PTR(x) being a particular

inst(x, y) being an instance of part(x, y) being a part of

Underlying logic: FOLUsual axioms characterize the primitives


SOME AXIOMS

(1) ~ (PTR(x) UN(x)), i.e. PTR(x)→ ~UN(x) (2) PTR(x) UN(x)

(Exclusivity, exhaustivity.)

(3) xy UN(x) → (PTR(y) inst(y,x))(4) xy PTR(x) → (UN(y) inst(x,y))

(No UN without some PTR; no PTR without some UN.)


SOME AXIOMS

(5) inst(x, y) → PTR(x) UN(y)(6) part(x, y) → PTR(x) PTR(y)

(Inst holds between particulars and universals. Part holds between particulars.)

Further axioms characterize part which we do not consider here.


GRANULARITY LEVELS

Let GRAN = <G1, G2, G3 …. G12> be a set of levels of granularity, ordered from coarsest to finest.

Let B be a set of biological particulars (e.g. of all the instances of universals defined by GO or FMA).


GRANULARITY LEVELS

We define gr as the function of B onto GRAN. This function associates each particular with its level of granularity.

gr: x gr(x)

for x B and gr(x) GRAN

Formalization of the Minimalist Approach

ADDING A PRIMITIVE:

GR(x) being a grain

ADDING AN AXIOM:

(7) GR(x) → PTR(x)

If something is a grain, then it is a particular.


DEFINITIONS:

A grain-universal

GR-UN(x) =: y(inst(y, x) → GR(y))

A grain-universal is an entity all instances of which are grains.


DEFINITIONS:

A granular-part:GRP(x)=: y (GR(y) part(x,y) gr(x)=gr(y))

A granular-part is an entity which is a part of a grain while both the entity and the grain

exist at the same level.


DEFINITIONS:

A granular-system in a weak sense:GRS(x)=: y (GR(y) part(y,x) gr(x)=gr(y))

A granular-system is an entity which has at least one grain as a part while both the

entity and the grain exist at the same level.


MODELS

To represent models for our axiomatic system we use modified Hasse diagrams:


MODELS


relation part(a,b)

b

a c

d

e


MODELS


property GRP(d)

b

a c

d

e

property GRS(c)property

GR(e)


A granular-system which has as its part one granule and one granular-part (without having as its part a granule of which this granular-part is a

part) would be an admissible model of GRS:

We might want to rule this model out.

To this end we define a granular-system in a strong sense.


DEFINITIONS:Granular-system in a strong sense:

GRS*(x) =: GRS(x) y z(GRP(y) part(y, x) → GR(z) part(y, z) part(z, x)

gr(x)=gr(y)= gr(z))

To be a granular-system in a strong sense is to be a granular system in the weak sense and to have

only those granular-parts which are parts of granules which are themselves parts of the given

granular-system.


AXIOMS (within the same level):

Grains are not parts of grains:

AG1: GR(x) → ~y(GR(y) part(x, y) gr(x)=gr(y))



From AG1 (grains are not parts of grains), it follows that grains do not include grains as

parts:

TG1: GR(x) → ~y(GR(y) part(y, x) gr(x)=gr(y))



We might consider even a stronger axiom concerning grains, e.g. that grains do not

overlap:

AG1’: GR(x) → ~y(GR(y) x≠y overlap(x, y) gr(x)=gr(y))



Every particular is either a grain or a granular-part or a granular-system (two versions: in a strong or weak sense):

AG2: PTR(x) → GR(x) GRP(x) GRS(x)

AG2’: PTR(x) → GR(x) GRP(x) GRS*(x)


AXIOMS of COMPOSITION (i.e. across granular levels)

AG3: x GR(x) & gr(x)=Gn & n > 1 y GR(y) & gr(y)=Gn-1 & part(x, y)

AG4: x GR(x) & gr(x)=Gn & n < k y GR(y) & gr(y)=Gn+1 & part(y, x)

(Grains are included in the higher-level grains and they also include lower-level grains; analogically for granular-parts and

granular-systems. These axioms are similar to those of minimalism: instead of inst we use here GR. )

Formal Differences between Minimalism and Maximalism

AG? (Maximalism): PTR(x) → GR(x) GRP(x)

AG2 (Minimalism): PTR(x) → GR(x) GRP(x) GRS(x)

THE CRUCIAL DIFFERENCE: Whereas maximalism admits particulars to be grains or granular-parts only, minimalism admits

them to be granular-systems as well.

V. Granularity in Physiology

Granularity in Physiology

Our examples so far included entities such as organs, cells, molecules … how is it

with granularity of functions and processes?

Continuants and Occurrents

Continuants Occurrents

independent dependent structures functions processes




Entities which continue through time (Broad 1933)





Entities which occur in time (Broad 1933)





Entities which occur in time (Broad 1933)

Entities which need/need not other entities for their existence (Husserl 1900)




Anatomy Physiology


functions processes

Physiology

Two suggestions:1. Granularity of functions and processes

is derived from the anatomical entities of which they are functions and processes.


functions processes

Physiology

Two suggestions:1. Granularity of functions and processes


2. Granularity is determined on the basis of parthood relations between processes.

Granularity in PhysiologyTwo suggestions:1. Granularity of functions and processes



For instance, DNA replication is a part of the NA-protein biosynthesis in the life-process of cells …


DNA DNA RNA

proteins

replication transcriptiontranslation

serve as enzymes in katalysis

buildin

g b

locks

of cells

NA-protein biosynthesis


DNA DNA RNA

proteins

replication transcriptiontranslation

serve as enzymes in katalysis

buildin

g b

locks

of cells


DNA replication

IS A PART OF?



DNA replication

IS A PART OF?

Perhaps.But since parthood does

not constitute granularity (Principle

8), there is no need to assign granularity

levels to processes and functions

independently of anatomical structures

which bear them.



Granularity in Physiology is

as easy as or

as difficult as Granularity in Anatomy

SummaryI. Accepted PrinciplesII. Controversial Principles:

A. Self-connectedness of GrainsB. Tissues as a Level of Granularity?C. Higher-order Granular Systems: Minimalism vs. Maximalism

III. FormalizationA. MaximalismB. Minimalism

IV. Notes on FMA, GO, SNOMED-CTV. Granularity in Physiology





II. Controversial Principles A. Self-connectedness of Grains

For maximalists: difficult to hold;

For minimalists: easy to hold since e.g. endocrine system is not a grain.





II. Controversial Principles B.Tissues as a Level of

Granularity?

For maximalists: controversial;• Kumar: tissues must be

represented;

• Smith: let’s get rid of them.

For minimalists: easy to represent as GRS while denying them the status of a granular level.





II. Controversial Principles C.Higher-order Gran. Systems

Maximalism vs. Minimalism

Advantages of maximalism: • less complicated formalization.

Advantages of minimalism: • easy to decide on gran. levels;• no badly-behaving levels; • authority of FMA.





III. Formalization A. Maximalism B. Minimalism

The crucial difference between the two:

Maximalism: Every particular is either a grain or a granular-part.

Minimalism: Every particular is either a grain or a granular-part or a granular-system.





IV. Notes on FMA, GO, SNOMED-CT

Foundational Model of Anatomy:

• Metaknowledge endorses minimalism, although it is not transparent in Anatomical Taxonomy

• it can be easily implemented, e.g. by introducing a further slot in Protége.





V. Granularity in Physiology

Granularity of functions and processes is derived from the

granularity of anatomical entities which bear them.

some issues in granularity daniel d. novotný ifomis workshop in freiburg, institute of medical...

Documents

level slide

granularity level

level of granularity

granularitylevel explosion

granular level of

levels of granularity

higher level

granularity daniel