Conceptual Modeling and Ontological Analysis

1
Conceptual Modeling and Ontological Analysis

• Nicola Guarino, LADSEB CNR,Italy
• Chris Welty, Vassar College, USA

2
Objectives

• Introduce the notions of formal ontology from
  Philosophy
• Present basic tools for ontology-driven
  conceptual analysis based on formal ontology
• Explore some principled guidelines for using
  these tools
• Discuss examples of using these guidelines and
  tools in practice

3
An Interdisciplinary Approach

• Towards a unified Ontology-driven Modelling
  Methodology for databases, knowledge bases and
  OO-systems
• Grounded in reality
• Transparent to people
• Rigorous
• General
• Based on
• Logic
• Philosophy
• (Linguistics)

4
Summary

• Ontology and ontologies
• Models and conceptualizations
• Ontology-driven conceptual modeling
• Formal ontological analysis
• Mereology
• Identity, unity, essence
• Essence and rigidity
• Identity and identity criteria
• Unity and unity criteria
• Dependence
• Using the formal properties
• Basic property kinds
• Further property kinds based on common ICs/UCs
• Ontology-driven modeling principles
• Taxonomic relationships
• An extended example
• Membership relationships
• Part-whole relationships
• A minimal top-level ontology

5
Ontology and ontologies
6
What is Ontology

• The study of being qua being the study of
  possible
• The study of the nature of possible ontology as
  the theory of distinctions among possibilia
• The study of the most general characteristics
  that anything must have in order to count as a
  (certain kind of) being or entity.

7
Definitions

• Ontology (capital o)
• a philosophical discipline.
• An ontology (lowercase o)
• specific artifact designed with the purpose of
  expressing the intended meaning of a vocabulary

8
What is an ontology?

• A shared vocabulary
• Plus A specification (actually, a
  characterization) of the intended meaning of that
  vocabulary
• ...i.e., an ontology accounts for the commitment
  of a language to a certain conceptualization
• An ontology is a specification of a
  conceptualization Gruber 95

9
Models and Conceptualizations
10
Capturing Intended Meaning

• First order logic is ontologically neutral
• Logical KBs often rely on natural language to
  convey intended meaning

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Intended Models
An ontology consisting of just a vocabulary is
of little use - Unintended interpretations need
to be excluded
12
What is a conceptualization?
Conceptualization of scene 1 lta, b, c, d, e ,
on, above, clear, table gt
13
What is a conceptualization?
The same conceptualization?
14
What is a conceptualization

• Conceptualization the formal structure of
  reality as perceived and organized by an agent,
  independently of
• the vocabulary used (i.e., the language used)
• the actual occurence of a specific situation
• Different situations involving the same objects,
  described by different vocabularies, may share
  the same conceptualization.

15
Relations vs. Conceptual Relations
(Montague-style semantics)
ordinary relations are defined on a domain
D conceptual relations are defined on a domain
space ltD, Wgt
16
Ontologies constrain the intended meaning
Conceptualization C
Commitment KltC,Igt
Language L
Models M(L)
17
Levels of Ontological Depth

• Lexicon
• Vocabulary with NL definitions
• Simple Taxonomy
• Thesaurus
• Taxonomy plus related-terms
• Relational Model
• Unconstrained use of arbitrary relations
• Fully Axiomatized Theory

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Our Framework Ontology-Driven Conceptual
Modeling
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Formal Ontology

• Theory of formal distinctions and connections
  within
• entities of the world, as we perceive it
  (particulars)
• categories we use to talk about such entities
  (universals)
• Basic tools of formal ontological analysis
• Theory of Parts and Wholes (Mereology)
• Theory of Identity, Integrity, Essence
• Theory of Dependence
• Why formal?
• Two meanings
• rigorous
• general
• Formal logic connections between truths -
  neutral wrt truth
• Formal ontology connections between things -
  neutral wrt reality Varzi 96
• Goal characterizing particulars and universals
  by means of formal properties and relations.

20
Approach

• Draw fundamental notions from Formal Ontology
• Establish a set of useful property kinds, based
  on behavior wrt above notions (meta-properties).
• Explore the constraints they impose on
  Information Systems design, and add further
  modeling principles
• Establish a minimal top-level ontology to drive
  conceptual modeling

21
Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
Minimal Top-Level Ontology
Ontology-Driven Modeling Principles
Useful Property Kinds
Formal Ontological Properties/Relations
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From Ontology to Data

• Reference ontology (development time)
• establishes consensus about meaning of terms
• Application ontology (development time)
• Focuses on a particular application
• limited by relevance choices related to a certain
  application
• Conceptual model (run time)
• implements an ontology (Tbox)
• Describes constraints between terms to be checked
  at run time (terminological services)
• limited by expressive power of implementation
  medium
• Database (Abox) (run time)
• Describes a specific (epistemic) state of affairs

23
Formal Ontological Analysis

• Mereology
• Identity, Unity, Essence
• Dependence

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Mereology
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Mereology

• A possible primitive proper part-of relation
  (PP)
• asymmetric
• transitive
• Pxy def PPxy ? xy
• Some further axioms

26
The problems withGeneral Extensional Mereology

• Generality of mereological sums
• Extensionality
• different identifying properties while having the
  same parts
• different parts while having the same identifying
  properties
• Admittability of atoms

27
Part, Constitution, and Identity

• Structure may change identity

• Extensionality is lost

• Constitution links the two entities

• Constitution is asymmetric (implies dependence)

a b
28
Identity, Unity, Essence
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Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
Minimal Top-Level Ontology
Ontology-Driven Modeling Principles
Useful Property Kinds
Formal Ontological Properties/Relations
?
30
Identity, Rigidity, Unity

• How can an entity change while keeping its
  identity?
• Under what conditions does an entity lose its
  identity?
• Do entities have any essential properties?
• Does a change of parts affect identity?
• When does an entity count as one?
• ...How do we know the answers

31
Identity and Unity

• Identity is this my dog?
• Unity is the collar part of my dog?

32
Essence and rigidity
33
Intuitive Rigidity

• Certain entities have essential properties.
• John must have a brain.
• John must be a person.
• Certain properties are essential to all their
  instances (compare being a person with having a
  brain).
• These properties are rigid - if an entity is ever
  an instance of a rigid property, it must always
  be.

34
Formal Rigidity

• f is rigid (R) ?x f(x) ? f(x)
• e.g. Person, Apple
• f is non-rigid (-R) ?x f(x) ? f(x)
• e.g. Red, Male
• f is anti-rigid (R) ?x f(x) ? f(x)
• e.g. Student, Agent

35
Identity and identity criteria
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Synchronic Identity Criteria

• Material objects same-location
• Immaterial objects same-location not valid any
  more...

37
Diachronic Identity

• Requires some notion of persistence
• In addition, the sameness (or continuity) of
  certain properties is required
• The castle/bunch of bricks
• Identity is not similarity

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A priori identity?

• Ultimately, identity criteria are the result
  ofour conceptualization of reality.
• They are always related to a class of entities
  considered as relevant for our purposes.
• In general, identity cant be defined.
• What we can have are just informative
  constraints.

39
Identity criteria

• Based on the sameness of a certain
  propertyf(x,t) ? f(y,t) ? ((c(x,z,t) ?
  c(y,z,t))? x y)
• t t synchronic t ? t diachronic
• Generalization
• f(x,t) ? f(y,t) ? (G(x,y, t ,t)? x y)

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Necessary ICs

• A formula G is a necessary IC for f if
• f(x,t) ? f(y,t) ? xy ? G(x,y,t,t)
• provided that
• it is not equivalent to universal identity
• ?xytt G(x,y,t,t) ? xy
• it is not trivially true of all fs
• ?xytt f(x,t) ? f(y,t) ? G(x,y,t,t)

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Sufficient ICs

• A formula G is a sufficient IC of f if
• f(x,t) ? f(y,t) ? G(x,y,t,t) ? xy
• provided that
• it is not equivalent to universal identity
• ?xytt G(x,y,t,t) ? xy
• it is not trivially false
• ?xytt G(x,y,t,t)

42
Identity Meta-Properties

• Carrying Identity (I)
• Having an IC, either own or inherited.
• Non-rigid properties must inherit ICs.
• e.g. has-same-fingerprint an IC for Person
• Supplying Identity (O)
• having an IC that is not carried by a subsuming
  property
• Only Rigid properties can supply ICs

43
Local Identity?

• Global IC Rigid properties
• Local IC (L) non-Rigid properties
• Local IC identifies instances of f only when they
  are instances of f
• same-wing-pattern for Butterfly
• nec suf but only when one entity is an instance
  of Butterfly, but not when that entity is a
  caterpillar
• same-registration-no. for students
• Only-suf Holds only when one entity is in a
  certain student experience
• Global IC identifies an entity for its entire
  existence (only for R properties)

44
Unity and Unity Criteria
45
Unity Analysis

• What counts as a whole? What makes it a whole?
• In which sense are its parts connected? What are
  the properties of the connection relation?
• How is the whole isolated from the background?
  What are its boundaries?
• What is the role played by the parts with respect
  to the whole?

46
Unity analysisand Mereotopology

• Primitive topological connection (C)
• Some axioms
• reflexivity
• symmetry
• monotonicity wrt parthood Pxy ? Cxz ? Cyz
• external contact everything is connected with
  its mereological complement
• Problems
• distinguish between open and closed regions?
• get rid of P, defining Pxy def Cxz ? Cyz ?
• different kinds of connection (line, point,
  surface) is C alone enough?

47
Unity Conditions

• An object a is a whole under w iff w is an
  equivalence relation such that
• P(y,a) ? P(z,a) ? w(y,z)
• but not
• w(y,z) ? ?x(P(y,x) ? P(z,x))
• ? can be seen as a generalized indirect connection

48
Conditions for Unity

• To achieve this we need
• a suitable connection relation - how do we get
  from one part to another?
• some notion of boundary - how do we know when to
  stop?

49
Unity and Plurality

• Strong vs. weak self-connection
• Piece of coal vs. lump of coal
• Basic component vs. assembly
• Surface connection vs. line or point connection
• Singular objects strongly self-connected (may be
  wholes or not)
• Plural objects sums of wholes
• Collections (the sum is not a whole)
• Plural wholes (the sum is also a whole)
• Mere sums

50
Unity Meta-Properties

• If all instances of a property f are wholes under
  the same relation, f carries unity (U)
• When at least one instance of f is not a whole,
  or when two instances of f are wholes under
  different relations, f does not carry unity (-U)
• When no instance of f is a whole, f carries
  anti-unity (U)

51
Disjointness Theorem
Properties with incompatible IC/UC are disjoint
52
Examples of identity and unity conditions

• An atom of matter
• An amount of matter
• A mass of matter
• A piece of coal
• A heap of coal
• A doughnut

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Dependence
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Dependence Analysis

• Can an entity exist alone?
• Does its existence imply the existence of
  something else? (rigid dependence)
• Does it imply the existence of some entities that
  are instances of a specific class? (generic
  dependence)
• Does a property holding for x depend on something
  else besides x? (property dependence)

55
Dependence Meta-Properties

• Our methodology currently uses only property
  dependence
• A property f is dependent (D) if
• ?x f(x) ? ?y j(y) ? P(x,y) ? C(x,y)
• If there is at least one instance of the property
  that is not dependent, the property is not
  dependent (-D)
• Also exclude qualities (i.e. Red), entities that
  necessarily exist (the universe), and subsumed
  properties.

56
Using the meta-properties
57
Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
?
Minimal Top-Level Ontology
Ontology-Driven Modeling Principles
Useful Property Kinds
Formal Ontological Properties/Relations
58
Motivation

• Our methodology will require analyzing all
  properties in an ontology according to these
  meta-properties This is a lot of work!
• Why perform this analysis?
• Makes modeling assumptions clear, which
• helps resolve known differences
• helps expose unknown differences

59
Resolving known Differences

• Two well-known ontologies define
• Physical object is-a amount of matter (WordNet)
• Amount of matter is a Physical Object (Pangloss)
• Which one is correct?
• Analyze each
• Physical-object
• Amount of matter
• Result
• According to the most common understanding, both
  ontologies are wrong, each concept is at the
  top-level

60
Exposing Unknown Differences

• Agreement
• An organization is a Social Entity
• Analysis
• Person 1 Social Entity OUR -D
• Person 2 Social Entity OUR D
• Problem?
• Person 1 A social entity is a group of people
  who are together for some social reason.
• Person 2 A social entity is an entity recognized
  by society, therefore D

61
Property Kinds
62
Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
Minimal Top-Level Ontology
Ontology-Driven Modeling Principles
Useful Property Kinds
?
Formal Ontological Properties/Relations
63
Basic Property kinds
64
Sortals, categories, and other properties

• Sortals (horse, triangle, amount of matter,
  person, student...)
• Carry identity
• Hardly definable in terms of a few primitives
• High organizational utility
• Categories (universal, particular, event,
  substance...)
• No identity
• Useful generalizations for sortals
• Characterized by a set of (only necessary) formal
  properties
• Good organizational utility
• Other non-sortals (red, big, decomposable,
  eatable, dependent, singular...)
• No identity
• Span across different sortals
• Limited organizational utility (but high semantic
  value)

65
A formal ontology of properties
Property
66
Basic Property Kinds Table
67
Further Property KindsCommon ICs/UCs
68
Ontological Levels

• Physical
• Atomic (a minimal grain of matter)
• Static (a configuration, a situation)
• Mereological (an amount of matter, a collection)
• Topological (a piece of matter)
• Morphological (a cubic block, a constellation)
• Functional (an artifact, a biological
  organ)
• Biological (a human body)
• Intentional (a person, a robot)
• Social (a company)
• Correspond to different kinds of IC/UC
• All levels except the mereological one have
  non-extensional IC
• A generic dependence relation links higher
  levels to their immediate inferior.

69
Identity and unity conditions
70
Ontology-driven Modeling Principles
71
Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
Minimal Top-Level Ontology
Ontology-Driven Modeling Principles
?
Useful Property Kinds
Formal Ontological Properties/Relations
72
Re-visiting abstraction relationships

• Taxonomic relationships (generalization)
• Membership relationships (association)
• Part-whole relationships (aggregation)

73
Taxonomic relationships
74
Subsumption Misused

• To express disjunction
• Person is-a Legal-Agent
• Company is-a Legal-Agent
• To express constitution
• Person is-a Amount of Matter
• To express multiple meanings
• Book is a physical-obect
• Book is a abstract-object

75
Assumptions

• No entity without identity
• Every entity must instantiate a rigid property
  with identity (a type)

76
Taxonomic Constraints

• R ? R
• -I ? I
• -U ? U
• U ? U
• -D ? D

• Incompatible ICs are disjoint
• Incompatible UCs are disjoint

For these we introduced Common UC/IC
77
Impact of taxonomic constraints on ontology
design

• Stratification replaces multiple inheritance in
  many cases
• Simpler taxonomies
• Moderate proliferation of individuals
• Co-localization of entities of different kind
• Non-taxonomic relations become important
• Dependence
• Co-localization
• Constitution
• Participation
• Type/role distinction allows for isolation of
  backbones in the taxonomic structure

78
Type and Role specialization

• Type specialization (e.g. Living being ? Person)
• New features affect identity
• Both necessary and sufficient ICs can be added
  while specializing types
• Polygon same edges, same angles
• Triangle two edges, one angle
• Living being same DNA, etc...
• Zebra same stripes
• Role specialization (e.g. Person ? Student)
• New features dont affect identity

79
Backbone Taxonomy

• The most important properties in a taxonomy are
  types, since all entities must instantiate at
  least one.
• The rigid properties above (categories) and below
  (quasi-types) types taken together form the most
  useful structure in a taxonomy - the backbone
  taxonomy

80
An extended example
81
Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
?
Minimal Top-Level Ontology
Ontology-Driven Modeling Principles
Useful Property Kinds
Formal Ontological Properties/Relations
82
Entity
83
Assign Meta-Properties
84
Property AnalysisEntity, Location

• Entity
• Everything is an entity
• -I-U-DR
• Category

• Location
• A generalized region of space.
• O by its parts (mereologically extensional).
• U no way to isolate a location
• -DR
• Type

85
Property AnalysisAmount of Matter, Red

• Amount of Matter
• unstructured /scattered stuff as lumps of clay
  or some bricks
• O mereologically extensional
• U intrinsically no unity
• -DR
• Type

• Red
• Really Red-thing, the set of all red-colored
  entities
• -I-U-D-R
• Formal Attribution

86
Property AnalysisAgent, Group

• Agent
• An entity playing a part in some event
• -I-U no universal IC/UC
• D on the event/action participating in
• R no instance is necessarily an agent
• Formal role

• Group
• An unstructured collection of wholes
• O same-members
• U unstructured, no unity.
• -DR
• Type

87
Property AnalysisPhysical Object, Living Being

• Physical Object
• Isolated material objects.
• O same spatial location (only synchronic, no
  common diachronic IC).
• U Topological
• -DR
• Type

• Living Being
• O same-DNA (only nec.)
• U biological unity
• -DR
• Type

88
Property AnalysisFood, Animal

• Food
• I-OU amt. of matter
• D something that eats it.
• R being food is not necessary...
• Material Role

• Animal
• O same-brain
• U biological unity
• -DR
• Type

89
Property AnalysisLegal Agent, Group of People

• Legal Agent
• A legally recognized entity
• L All legal systems have a defined IC,
  has-same-legal-ID
• -U no universal unity
• D on the legal body that recognizes it
• R not necessary
• Material Role

• Group of People
• See Group
• I-OU-DR
• Quasi-type

90
Property AnalysisSocial Entity, Organization

• Social Entity
• A group of people together for social reasons
• -I no universal IC
• U social-connection
• -DR
• category

• Organization
• A group of people together, with roles that
  define some structure
• O same-mission and way of operating
• U functional
• -DR
• Type

91
Property AnalysisFruit

• Fruit
• An individual fruit, such as an orange or bannana
• O same-plant, same-shape, etc. (only nec.)
• U topological
• -DR
• Type

92
Property AnalysisApple, Red Apple

• Apple
• O shape, color, skin pattern (only nec)
• U topological
• -DR
• Type

• Red-Apple
• I-O from Apple
• U from Apple
• -D
• R no red apple is necessarily red
• type-attribution mixin

93
Property AnalysisVertebrate, Person

• Vertebrate
• Really vertebrate-animal
• A biological classification that adds new
  membership criteria (has-backbone)
• I-O from animal
• U from animal
• -DR
• quasi-type

• Person
• O same-fingerprint
• U from animal
• -DR
• Type

94
Property AnalysisButterfly, Caterpillar

• Butterfly
• L same-wing-pattern
• U biological
• -D
• R the same entity can be something else (a
  caterpillar)
• Phased sortal

• Caterpillar
• L spots, legs, color
• U biological
• -D
• R caterpillars become butterflies and change
  their IC
• Phased sortal

95
Property AnalysisCountry

• Country
• A place recognized by convention as autonomous
• L government, sub-regions
• U countries are countable (heuristic)
• -D
• R some countries do not exist as countries any
  more (e.g. Prussia) but are still places
• Phased sortal

96
Entity-I-U-DR
Remove non-rigid properties
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Agent -I-UDR
Red -I-U-D-R
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Food I-OUDR
Fruit OU-DR
Animal OU-DR
Legal agent L-UDR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Red apple I-OU-DR
Country LU-DR
Person OU-DR
97
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• U cant subsume U
• Living being can change parts and remain the
  same, but amounts of matter can not (incompatible
  ICs)
• Living being is constituted of matter

Group OU-DR
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
98
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• U cant subsume U
• Living being can change parts and remain the
  same, but amounts of matter can not (incompatible
  ICs)
• Living being is constituted of matter

Group OU-DR
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
99
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• U cant subsume U
• Physical objects can change parts and remain the
  same, but amounts of matter can not (incompatible
  ICs)
• Physical object is constituted of matter

Group OU-DR
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
100
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• U cant subsume U
• Physical objects can change parts and remain the
  same, but amounts of matter can not (incompatible
  ICs)
• Physical object is constituted of matter

Group OU-DR
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
101
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• Meta-properties fine
• Rigidity-check fails when an entity stops being
  an animal, it does not stop being a physical
  object (when an animal dies, its body remains)
• Constitution again

Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
102
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• Meta-properties fine
• Rigidity-check fails when an entity stops being
  an animal, it does not stop being a physical
  object (when an animal dies, its body remains)
• Constitution again

Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
103
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• U cant subsume U
• A group, and group of people, cant change parts
  - it becomes a different group
• A social entity can change parts - its more than
  just a group (incompatible IC)
• Constitution again

Group OU-DR
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
104
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• U cant subsume U
• A group, and group of people, cant change parts
  - it becomes a different group
• A social entity can change parts - its more than
  just a group (incompatible IC)
• Constitution again

Group OU-DR
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
105
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Physical object OU-DR
Living being OU-DR

• U cant subsume U
• Same as for social entity.
• Note also the same group can constitute different
  organizations.

Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
106
Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Physical object OU-DR
Living being OU-DR

• U cant subsume U
• Same as for social entity.
• Note also the same group can constitute different
  organizations.

Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
107
Entity-I-U-DR
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Physical object OU-DR
Living being OU-DR
Group of people I-OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
108
Entity-I-U-DR
Analyze Phased Sortals
Amount of matter OU-DR
Location O-U-DR

• For phased sortals what do they phase into?
• Country is anti-rigid because it is representing
  multiple senses of country a geographical region
  and a political entity.
• Split the two senses into two concepts, both
  rigid, both types.

Group OU-DR
Physical object OU-DR
Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Organization OU-DR
Person OU-DR
109
Entity-I-U-DR
Analyze Phased Sortals
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Physical object OU-DR

• There is an relationship between the two, but not
  subsumption.

Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Country LU-DR
Organization OU-DR
Person OU-DR
110
Entity-I-U-DR
Analyze Phased Sortals

• Caterpillar phases into butterfly - a true phased
  sortal
• There must be some property from which a single
  entity can uniquely claim identity across phases

Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• Define a rigid property which subsumes only the
  phases of the same entity.

Physical object OU-DR
Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Organization OU-DR
Person OU-DR
111
Entity-I-U-DR
Analyze Phased Sortals
Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• Try for a type, may be quasi.
• IC for Lepidopteran could be same-cocoon

Physical object OU-DR
Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
112
Entity-I-U-DR
Analyze Roles
Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• R cant subsume R
• Really want a type restriction all agents are
  animals or social entities.
• Subsumption is not disjunction!

Physical object OU-DR
Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
113
Entity-I-U-DR
Analyze Roles
Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• R cant subsume R
• Really want a type restriction all agents are
  animals or social entities.
• Subsumption is not disjunction!

Agent -I-UDR
Physical object OU-DR
Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
114
Entity-I-U-DR
Analyze Roles
Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• R cant subsume R
• Another disjunction all legal agents are
  countries, persons, or organizations

Agent -I-UDR
Physical object OU-DR
Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
115
Entity-I-U-DR
Analyze Roles
Amount of matter OU-DR
Location O-U-DR
Group OU-DR

• R cant subsume R
• Another disjunction all legal agents are
  countries, persons, or organizations

Agent -I-UDR
Physical object OU-DR
Living being OU-DR
Legal agent L-UDR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
116
Entity-I-U-DR
Analyze Roles
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Agent -I-UDR

• R cant subsume R
• Apple is not necessarily food. A poison-apple,
  e.g., is still an apple.
• U cant subsume U
• Caterpillars are wholes, food is stuff.

Physical object OU-DR
Living being OU-DR
Legal agent L-UDR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
117
Entity-I-U-DR
Analyze Roles
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Agent -I-UDR

• R cant subsume R
• Apple is not necessarily food. A poison-apple,
  e.g., is still an apple.
• U cant subsume U
• Caterpillars are wholes, food is stuff.

Physical object OU-DR
Living being OU-DR
Legal agent L-UDR
Food I-OUDR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
118
Entity-I-U-DR
Analyze Attributions
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Agent -I-UDR

• No violations
• Attributions are discouraged, can be confusing.
• Often better to use attribute values (i.e. Apple
  Color red)

Physical object OU-DR
Living being OU-DR
Legal agent L-UDR
Food I-OUDR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
119
Entity-I-U-DR
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Agent -I-UDR
Physical object OU-DR
Living being OU-DR
Legal agent L-UDR
Food I-OUDR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
120
Entity-I-U-DR
The backbone taxonomy
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Physical object OU-DR
Living being OU-DR
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Organization OU-DR
Person OU-DR
121
Entity-I-U-DR
Amount of matter OU-DR
Location O-U-DR
Group OU-DR
Agent -I-UDR
Physical object OU-DR
Living being OU-DR
Food I-OUDR
Legal agent L-UDR
Red -I-U-D-R
Social entity -IU-DR
Fruit OU-DR
Animal OU-DR
Group of people I-OU-DR
Apple OU-DR
Lepidopteran OU-DR
Vertebrate I-OU-DR
Geographical Region O-U-DR
Country OU-DR
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
Red apple I-OU-DR
122
Membership relationships
123
Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
Minimal Top-Level Ontology
Ontology-Driven Modeling Principles
?
Useful Property Kinds
Formal Ontological Properties/Relations
124
Singular vs. Plural

• Singular objects strongly self-connected
• Plural objects
• Collections
• Plural wholes
• Mere sums

125
The Instance-of Relation (1)

• Being instance-of something vs. being an
  instance.
• The problems of logical predication
• x is an apple ? Apple(x)
• x is red ? Red(x)
• Instance-of vs. class membership
• John is a member of Person ? Person(John)
• Tree1 is a member of TheForest ?
  TheForest(Tree1) ??(violates usual intended
  interpretation of unary predicates property
  shared by all instances of the corresponding
  class. Doesnt pass the is-a test )
• Temporal instances
• Beethoven isnt an ultimate instance, since
  the young Beethoven may be an instance of it...

126
The Instance-of Relation (2)

• How to decide whether something is an instance?
• Properties can be instances of meta-properties
• Hence, being an instance may be a subjective
  property
• But being a particular IS NOT!
• Particulars are always ultimate instances.
• Concrete entities are always particulars.
• So-called temporal instances are either
  temporal parts of a particular or instances of an
  abstract class.

127
Part-whole relationships
128
Part-of vs. part-whole relations

• component/integral object
• member/collection
• portion/mass
• stuff/object
• place/area
• feature/activity

129
Framework
Conceptual Model
Conceptualization
Ontology
User
Methodology
Minimal Top-Level Ontology
?
Ontology-Driven Modeling Principles
Useful Property Kinds
Formal Ontological Properties/Relations
130
A Minimal Top-level Ontology

• Entity
• Particular
• Concrete particular
• Location
• Object
• Abstract particular
• Set
• Structure
• Universal
• Property
• Property Kinds...
• Relation

131
Well-Founded OntologiesSome Basic Design
Principles

• Be clear about the domain
• particulars (individuals)
• universals (classes and relations)
• linguistic entities (nouns, verbs, adjectives...)
• Take identity seriously
• different identity criteria imply disjoint
  classes
• Isolate a basic taxonomic structure
• only sortals like person (as opposite to
  red) are good candidates for being taxons
• Make an explicit distinction between types and
  roles (and other property kinds)

132
Ontologists Wanted!
133
FOIS 2001Formal Ontology in Information Systems
Announcing...

• Check out www.fois.org