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Conceptual Modeling and Ontological Analysis

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Title: 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

11
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

18
Our Framework Ontology-Driven Conceptual
Modeling
19
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
22
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

24
Mereology
25
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
29
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
36
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

38
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)

40
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)

41
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

53
Dependence
54
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
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