Rules for Good Ontology

1
Rules for Good Ontology

• Rules of thumb
• represent ideals to be approximated to in
  practice
• often with trade-offs

2
The ontologists job

• is not to mimic or replace or usurp science
• not to discover statistical or functional laws
• it is to establish the categories involved in
  given domains of reality and the relations
  between them
• via taxonomies
• and partonomies
• and NORMATIVE ISSUES

3
Naturalness

• A good ontology should include in its basic
  category scheme only those categories which are
  instantiated by entities in reality (it should
  reflect nature at its joints)

4
A good first test

• the categories in question should be reflected
  in TEE
• (for Technically Extended English
• English as extended by the various technical
  vocabularies of medical and scientific
  disciplines)

5
Basic categories

• reflected by morphologically simple terms
• dog
• pain
• foot
• blood
• hunger
• hot
• red
• diabetes

6
No theoretical artifacts

• A good ontology should not include in its basic
  category scheme
• artifacts of logical, mathematical or
  philosophical theories (such as transfinite
  cardinals, instantaneous rabbit-slices,
  non-existent golden mountains, functions across
  possible worlds, and the like).

7
A good category scheme

• should not be a mish-mash of natural and
  philosophical taxa
• (keep views separate
• basic views, domain-specific views,
• theoretical-artefactual views)

8
Problem of Double-Counting

• in realm of substances
• foot, arm, nose
• family, patient population
• fiat parts and aggregates on the same level of
  granularity should be explicitly marked as
  involving double-counting

9
Cheese-paring principle

• While a good ontology should use categories
  which reflect only TEE, it should also have the
  resources to do justice to the fact that the
  world can be sliced in many ways, including ways
  not reflected by TEE

10
Example of cheese-paring
substance
action (relational process)
substance
agent (substance plus role)
patient (substance plus role)
linked by mutual dependence
11
Always ask the question

• when is this proposition true?
• when does this entity exist?
• Two sorts of answers
• at t (for SNAP entities)
• over time interval t
• -------------------------------------------
• looking down on the order of time from the
  outside (for SPAN entities)

12
John lived in Kansas for 25 years

• when is this proposition true?
• when does the entity which makes it true exist?

13
Summing within SPAN and summing within SNAP are
both acceptable

• John plus his role Major John
• John plus his quality hungry John
• The rest of the World Cup

14
Confess Double-Counting

• in realm of substances
• ear, nose, throat, arm
• family, clinical trial population
• fiat parts and aggregates on the same level of
  granularity should be explicitly marked as
  involving double-counting

15
SNAPshot ONTOLOGY
16
Confess Double-Counting

• in realm of processes
• beginning, end, first phase
• series of clinical trials, World Cup
• fiat parts and aggregates on the same level of
  granularity should be explicitly marked as
  involving double-counting

17
SPAN ONTOLOGY
18
SPAM ONTOLOGY
19
No Crossing Categories

• If C is a major category then an instance of C is
  always an instance of C whichever VIEW of C we
  take
• If C is a major category then an instance of C is
  always an instance of C whichever granularity we
  take

20

• If x instances a category under any determinable,
  then it instances this category under all
  determinables
• Johns temperature is a SNAP entity
• The value of Johns temperature is 62 degrees
• (The value is changing all the time)

21
No others

• All category labels should be positive

22
Respect Granularity
spatial region
quality
substance
parts of spatial regions are always spatial
regions
23
Respect Granularity
spatial region
quality
substance
parts of substances are always substances
24
Respect Granularity
spatial region
quality
substance
parts of qualities are always qualities
25
Relations crossing the SNAP/SPAN border are not
part-relations
Johns life
26
Rule for Crossing Granularities

• For x and y instances of basic categories
• If x is part of y, then x is of the same category
  as y
• (if x is substantial, then y is substantial)
• (if x is a quality, then y is a quality)
• (if x is a process, then y is process)
• (if x is a spatial region, then y is a spatial
  region)
• (if x is a spatial boundary, then y is a spatial
  boundary)

27
Rule for Crossing Granularities

• For x an instances of a basic category, x is
  always an instance of that category in every view
  or from every perspective
• (if x is substantial, then y is substantial)
• (if x is a quality, then y is a quality)
• (if x is a process, then y is process)
• (if x is a spatial region, then y is a spatial
  region)
• (if x is a spatial boundary, then y is a spatial
  boundary)

28
How to treat cross-categorial structures?

• which ontology do they belong to?
• How to treat higher-order attributions
• Universals have instances
• Universal A depends for its instantiation on the
  instantiation of universal B
• Roughly these are meta-assertions
• (that they have special truthmakers of their own
  is an illusion of language)

29
Universals have instances

• is not an extra assertion
• rather it is something which shows itself via the
  syntax of a good ontological language
• (cf. Wittgensteins Tractatus)

30
Rules for good syntax in formalizing ontology

• entities of the same category should be
  represented in the language of ontology by means
  of symbols of the same type
• some symbols will not represent entities at all
  ()

31
Tools are just tools

• If specific logical or mathematical or
  conceptual tools are needed, for example for
  semantic purposes,
• then these should be clearly recognized as tools
  and thus not be seen as having consequences for
  basic ontology.
• (Possible worlds )

32
Trade off between cheese-paring and sake-mongering

• We say
• For Pierres sake , for Heinrichs sake
• But
• There are no sakes in this room
• This is so however we slice the cheese

33
Problems arise for partial ontologies

• only if they come along with the claim to be
  complete
• (reductionists are nearly always correct in what
  they hold to exist --
• but incorrect when they hold that nothing else
  exists)

34
Even reductionists

• are right as far as they go
• (even their peculiar maps of reality,
• as consisting of processes,
• or of spacetime worms,
• are transparent to reality)
• The only problem with such maps is that they are
  not complete

35
Rules Governing Taxonomies

• Every (coherent, tested) ontology for a given
  domain at a given level of granularity
• should be representable as a tree in the
  mathematical sense

36
Natural scientific classifications are principled
37
Principled classifications satisfy the
no-diamonds rule

• A E
• F
  G
• B C D
• 
  H

Good
Bad
38
Counterexample in the realm of artifacts ?
39
Eliminating counter-examples
urban structures
buildings
parking areas
multi-story car-parks
Ontoclean
40
No others

• A good taxonomy should contain no taxons labeled
• others

41
Representations

• A representation is never identical with the
  object which it is a representation of

42
Fallibilism

• Ontologists are seeking principles that are true
  of reality,
• but this does not mean that they have special
  powers for discovering the truth.
• Ontology is, like physics or chemistry, part of
  a piecemeal, on-going process of exploration,
  hypothesis-formation, testing and revision.

43
Fallibilism

• Ontological claims advanced as true today may
  well be rejected tomorrow in light of further
  discoveries or new and better arguments
• Ontology is like a small window on reality
  which, in fits and starts, gets bigger and more
  refined as we proceed

44
Adequatism

• A good ontology should be adequatist
• its taxonomies and partonomies should comprehend
  the entities in reality at all levels of
  aggregation,
• from the microphysical to the cosmological,
• and including also the middle world (the
  mesocosmos) of human-scale entities in between.
• Adequatists Aristotle, Ingarden, Chisholm

45
Nothing in life is certain

• except
• death
• and taxes
• Fictionalism is always wrong
• Either an entity exists, or it does not exist
• Either an entity type exists, or it does not exist

46
Quine is wrong

• There is no entity without identity
• We have no identity criteria for
• people
• taxes
• plans
• diseases

47
A good category scheme

• should not be a mish-mash of individuals and
  universals
• Universals are not extra types of entities
• Types of entities ARE universals
• Boxes in category diagrams represent universals
• The instances are what the boxes contain

48
SNAPshot ONTOLOGY
49
SNAPshot ONTOLOGY
50
Tree structure

• Higher nodes within the tree represent more
  general universals, lower nodes represent less
  general universals.

51

• Branches connecting nodes represent the
  relations of inclusion of a lower category in a
  higher
• man is included in mammal
• mammal is included in animal
• and so on.

52
An Ontology (Taxonomy) should be Principled

• Suppose that in counting off the cars passing
  beneath you on the highway, your checklist
  includes one box labeled red cars and another box
  labeled Chevrolets.
• The resultant inventory will be unprincipled
• you will almost certainly be guilty of counting
  some cars twice.
• Unprincipled the two modes of classification
  belong to two distinct classifications made for
  two distinct purposes

53

Tree structure implies

• A good ontology should satisfy certain
  well-formedness rules

54
Well-formedness rule

• Each tree is unified
• in the sense that it has a single top-most or
  maximal node, representing the maximum category
• comprehending all the categories represented by
  the nodes lower down the tree

55
Why trees?

• A taxonomy (ontology) with two maximal nodes
  would be in need of completion by some extra,
  higher-level node representing the union of these
  two maxima.
• Otherwise it would not be one taxonomy at all,
  but rather two separate taxonomies (e.g. SNAP and
  SPAN)

56
Entity

• label for the highest-level category of
  ontology.
• Everything which exists is an entity
• Alternative top-level terms favored by different
  ontologists thing, object, item,
  element, existent.
• Use of entity is dangerous (see Frege)

57
Basis in minimal nodes (leaves)

• Leaves of the tree represent the lowest
  categories (infima species)
• categories in which no sub-categories are
  included.
• Has a basis in minimal nodes the categories
  at the lowest level of the tree exhaust the
  maximum category

58
Exhaustiveness

• The chemical classification of the noble gases is
  exhausted by
• Helium, Neon, Argon, Krypton, Xenon and Radon.
• normally very hard to achieve

59
For a taxonomy with a basis in minimal nodes

• every intermediate node in the tree is
  identifiable as a combination of minimal nodes.

60
More well-formedness principles

• There should be a finite number of steps between
  the maximal category and each minimal category.
• There should be the same number of steps between
  the topmost node of the tree and all its
  lowest-level nodes.

61
Well-Formedness

• The taxonomy as a whole is thereby divided into
  homogeneous levels,
• each level represents a jointly exhaustive and
  pairwise disjoint partition of the corresponding
  domain of categories on the side of objects in
  the world.

62
Which rules satisfied by BFO?
63
Types of Formal Relation

• Intracategorial
• Mereological (part)
• Topological (connected, temporally precedes)
• Dependency
• Intercategorial
• Inherence (quality of)
• Location
• Participation (agent)

64
Relations can also hold across granularities

• Microbial processes in the human body sustain the
  human body in existence
• Neurophysiological processes in the brain cause
  and provide the substratum for cognitive processes

65
Trees of universals (species-genus hierarchies)

• capture the way the world is (realism)
• they depict the invariant
  structures/patterns/regularities in reality

66
or species-genus hierarchies

• may capture the way the world should be
• by depicting the structures/patterns/regulariti
  es in the realm of standards, ideal cases,
  recipes
• (a hierarchy of medical therapies)

67
Anglocentric (Aristotelian) Realism

• The general terms of TEE (or many of them),
• including terms like Coca Cola,
• correspond to universals (species and genera,
  invariant patterns) in reality

68
Two distinct realms of being
universals particulars
general individual
types tokens
species instances
essence fact
69
species, genera
mammal
frog
instances
70
Common nouns
common nouns proper names
71
types
mammal
frog
tokens
72
Accidents Species and instances
types
tokens
73
There are universals

• both among substances (man, mammal)
• and among qualities (hot, red)
• and among processes (run, movement)
• There are universals also among spatial regions
  (triangle, room, cockpit)
• and among spatio-temporal regions (orbit)

74
Substance universals

• pertain to what a thing is at all times at which
  it exists

cow man rock planet VW Golf
75
Quality universals

• pertain to how a thing is at some time at which
  it exists

red hot suntanned spinning
Clintophobic Eurosceptic
76
Process universals

• reflect invariants in the spatiotemporal world
  taken as an atemporal whole
• football match
• course of disease
• exercise of function
• (course of) therapy

77
Processes and qualities, too, instantiate genera
and species

• Thus process and quality universals form trees

78
Accidents Species and instances
quality
color
red
scarlet
R232, G54, B24
this individual accident of redness (this
token redness here, now)
79

• - IS-WE-STATE-OF
• This is a link which relates a STATE of a
  PROPERTY to the element where this STATE
  inherence.
• Example TEMPERATURE (is the property)
•                HIGH TEMPERATURE (is a state of
  the property TEMPERATURE)
•                HOT WATER   HAS-WE-STATE   HIGH
  TEMPERATURE (But at the level of the instance the
  reverse link can also be applied "high
  temperature 1" IS-WE-STATE-OF "hot water 1)

80

•   HAS-EXISTENT
• This link relates a process of existence to the
  entity that exists.
• Example MEDICAL HISTORY (is considered an
  EXISTANCE IN THE PAST) and HAS-EXISTENT a
  HEALTHCARE PHENOMENOM
• So "history of diabetes" is (for us) an
  "existence of diabetes in the past" and
  "diabetes" is the entity which existed.

81

• -         HAS-SAYING
• This is a link which relates a COMMUNICATIVE
  PROCESS (mental process) to the element which is
  communicated.
• Ex MENTION OF ABSCESS HAS-SAYING ABSCESS
•  -        HAS- SENSOR
• Relates an INTERNAL MENTAL PROCESS ( thinking,
  observation...) to the person/animal who performs
  this action
• Ex (at instance level) "John recognizes Mary."
  becomes "recognizing process 1" HAS-SENSOR "John
  1"

82

• -  HAS-PHENOMENON
• Also for  INTERNAL MENTAL PROCESS, but phenomenon
  is the entity which has been "perceived". (Mary
  in the example above)
• Ex DETERMINATION OF PROGNOSIS HAS-PHENOMENON
  PROGNOSIS

83

• -        HAS-SYSTEMIC-MEDIUM
• Relates a MATERIAL PROCESS to an entity which
  participates is the process in an active and
  passive way at the same time
• EX ARM INFLAMMATION HAS-SYSTEMIC-MEDIUM ARM or
  CHANGE IN WEIGHT HAS-SYSTEMIC-MEDIUM WEIGHT

84

• -       HAS-CEN-OCCURENCE-DURING
• Temporal link that indicates the event in
  question has happened (begun and ended) during
  the reference event.
• Ex INFARCT DURING SURGERY HAS-CEN-OCCURENCE-DURI
  NG SURGICAL DOING

85
Perspectivalism

• Perspectivalism

Different partitions may represent cuts through
the same reality which are skew to each other
86
Ontology

• like cartography
• must work with maps at different scales and with
  maps picking out different dimensions of
  invariants

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Varieties of granular partitions

• Partonomies inventories of the parts of
  individual entities
• Maps partonomies of space
• Taxonomies inventories of the universals
  covering a given domain of reality