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Ontological Analysis of Taxonomic Relationships. Nicola Guarino, LADSEB-CNR,Italy Chris Welty, Vassar College, USA. Thanks to: Bill Andersen, Pierdaniele Giaretta, Dario Maguolo, Claudio Masolo, Chris Partridge, Mike Uschold, Achille Varzi. Approach.

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ontological analysis of taxonomic relationships

Ontological Analysis of Taxonomic Relationships

Nicola Guarino, LADSEB-CNR,Italy

Chris Welty, Vassar College, USA

Thanks to: Bill Andersen, Pierdaniele Giaretta, Dario Maguolo, Claudio Masolo, Chris Partridge, Mike Uschold, Achille Varzi

approach
Approach
  • Draw fundamental notions from Formal Ontology
  • Establish a set of useful meta-properties, based on behavior wrt above notions
  • Explore the way these meta-properties combine to form relevant property kinds
  • Explore the taxonomic constraints imposed by these property kinds.
dealing with ontological relativism
Dealing withOntologicalRelativism
  • Deciding about the meta-properties carried by a given property…

Is up to YOU!

  • But a common agreementmust be achieved about the formal meaning (and practical utility) of meta-properties
what is a taxonomic relationship
What is a taxonomic relationship?
  • Is-a, a-kind-of, specialization-of, subclass (Brachman, 1983)
    • “horse is a mammal”
  • Helps deal with complexity
  • What does it mean?
    • x f(x) r(x) *

* note correction, page 210, formula (1)

ontology driven conceptual modeling
Ontology-driven conceptual modeling

Conceptual Model

Conceptualization

Ontology

User

Methodology

Minimal Top-Level Ontology

Ontology-Driven Modeling Principles

Useful Property Kinds

Formal Ontological Properties/Relations

essence and rigidity
Essence and 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.
formal rigidity
Formal Rigidity
  • f is rigid (+R): x f(x) f(x)
    • e.g. Person, Apple
  • f is non-rigid (-R): xf(x)  ¬f(x)
    • e.g. Red, Male
  • f is anti-rigid (~R): x f(x)  ¬f(x)
    • e.g. Student, Agent
rigidity constraint
Rigidity Constraint

+R  ~R

  • Why?
    • x P(x) Q(x)

Q~R

P+R

O10

identity and unity
Identity and Unity
  • Identity: is this my dog?
  • Unity: is the collar part of my dog?
identity criteria
Identity criteria
  • Classical formulation:

f(x)f(y)  (r(x,y) x = y)

  • Generalization:

f(x,t)f(y,t’)  (G(x,y,t,t’) x = y)

(synchronic: t= t’ ; diachronic: t≠ t’)

  • In most cases, G is based on the sameness of certain characteristic features:

G(x,y, t,t’)= z (c(x,z,t) c(y,z,t’))

a stronger notion global ics
A Stronger Notion:Global ICs
  • Local IC:f(x,t)f(y,t’)  (G(x,y,t,t’) x = y)
  • Global IC (rigid properties only):

f(x,t) (f(y,t’) G(x,y,t,t’) x = y)

identity conditions along taxonomies
Identity Conditions along Taxonomies
  • Adding ICs:
    • Polygon: same edges, same angles
      • Triangle: two edges, one angle
        • Equilateral triangle: one angle
  • Just inheriting ICs:
    • Person
      • Student
identity meta properties
Identity meta-properties
  • Supplying (global) identity (+O)
    • Having some “own” IC that doesn’t hold for a subsuming property
  • Carrying (global) identity (+I)
    • Having an IC (either own or inherited)
  • Not carrying(global) identity (-I)
identity disjointness constraint
Identity Disjointness Constraint

Besides being used for recognizing sortals, ICs impose constraints on them, making their ontological nature explicit:

Properties with incompatible ICs are disjoint

  • Examples:
  • sets vs. ordered sets
  • amounts of matter vs. assemblies
unity criteria
Unity Criteria
  • An object xis a whole under w iff w is an equivalence relation that binds together all the parts of x, such that

P(y,x)  (P(z,x)  w(y,z))

but not

w(y,z)  x(P(y,x)  P(z,x))

  • P is the part-of relation
  •  can be seen as a generalized indirect connection
unity meta properties
Unity Meta-Properties
  • If all instances of a property f are wholes under the samerelation, 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)
unity disjointness constraint
Unity Disjointness Constraint

Properties with incompatible UCs are disjoint

property dependence
Property Dependence
  • Does a property holding for x depend on something else besides x? (property dependence)
    • P(x)  y Q(y)
    • y should not be a part of x
  • Example: Student/Teacher, customer/vendor
sortals categories and other properties
Sortals, categories, and other properties
  • Sortals (horse, triangle, amount of matter, person, student...)
    • Carry identity
    • Usually correspond to nouns
    • High organizational utility
    • Main subclasses: types and roles
  • 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
    • Correspond to adjectives
    • Span across different sortals
    • Limited organizational utility (but high semantic value)
a formal ontology of properties
A formal ontology of properties

Category +R

Non-sortal

-I

Attribution -R-D

Role

~R+D

Formal Role

Property

Material role

Anti-rigid

~R

Non-rigid

-R

Phased sortal -D +L

Mixin -D

Sortal+I

Type +O

Rigid

+R

Quasi-type -O

the backbone taxonomy
The Backbone Taxonomy
  • Assumption: no entity without identity
  • Since identity is supplied by types, every entity must instantiate a type
  • The taxonomy of types spans the whole domain
  • Together with categories, types form the backbone taxonomy, which represents the invariant structure of a domain (rigid properties spanning the whole domain)
taxonomic constraints
+R  ~R

-I  +I

-U  +U

+U  ~U

-D  +D

Incompatible IC’s are disjoint

Incompatible UC’s are disjoint

Taxonomic Constraints
  • Categories subsume everything
  • Roles can’t subsume types
dealing with ontological relativism27
Dealing withOntologicalRelativism
  • Deciding about the meta-properties carried by a given property…

Is up to YOU!

  • But a common agreementmust be achieved about the formal meaning (and practical utility) of meta-properties
slide28

Amount of matter

Location

Group

Agent

Red

Physical object

Living being

Group of people

Food

Fruit

Animal

Legal agent

Apple

Vertebrate

Caterpillar

Red apple

Butterfly

Country

Person

Entity

assign meta-properties

Social entity

Organization

slide29

Entity-I-U-D+R

Remove non-rigid properties

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

Agent

-I-U+D~R

Red

-I-U-D-R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Food

+I-O~U+D~R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Legal agent

+L-U+D~R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Red apple

+I-O+U-D~R

Country

+L+U-D~R

Person

+O+U-D+R

slide30

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • ~U can’t 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

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide31

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • ~U can’t 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

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide32

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • ~U can’t 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

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide33

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • ~U can’t 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

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide34

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • Meta-properties fine
  • Identity-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

Group

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide35

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • Meta-properties fine
  • Identity-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

Group

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide36

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • ~U can’t subsume +U
  • A group, and group of people, can’t change parts - it becomes a different group
  • A social entity can change parts - it’s more than just a group (incompatible IC)
  • Constitution again

Group

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide37

Entity-I-U-D+R

Analyze taxonomic links

Amount of matter

+O~U-D+R

Location

+O-U-D+R

  • ~U can’t subsume +U
  • A group, and group of people, can’t change parts - it becomes a different group
  • A social entity can change parts - it’s more than just a group (incompatible IC)
  • Constitution again

Group

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide38

Entity-I-U-D+R

Location

+O-U-D+R

Amount of matter

+O~U-D+R

Group

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Group of people

+I-O~U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Apple

+O+U-D+R

Vertebrate

+I-O+U-D+R

Organization

+O+U-D+R

Person

+O+U-D+R

slide39

Entity-I-U-D+R

Agent

-I-U+D~R

Analyze Roles

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

  • ~R can’t subsume +R
  • Really want a type restriction: all agents are animals or social entities.
  • Subsumption is not disjunction!

Physical object

+O+U-D+R

Living being

+O+U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide40

Entity-I-U-D+R

Analyze Roles

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

  • ~R can’t subsume +R
  • Really want a type restriction: all agents are animals or social entities.
  • Subsumption is not disjunction!

Agent

-I-U+D~R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide41

Entity-I-U-D+R

Legal agent

+L-U+D~R

Analyze Roles

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

  • ~R can’t subsume +R
  • Another disjunction: all legal agents are countries, persons, or organizations

Agent

-I-U+D~R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide42

Entity-I-U-D+R

Analyze Roles

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

  • ~R can’t subsume +R
  • Another disjunction: all legal agents are countries, persons, or organizations

Agent

-I-U+D~R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Legal agent

+L-U+D~R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide43

Entity-I-U-D+R

Food

+I-O~U+D~R

Analyze Roles

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

Agent

-I-U+D~R

  • ~R can’t subsume +R
  • Apple is not necessarily food. A poison-apple, e.g., is still an apple.
  • ~U can’t subsume +U
  • Caterpillars are wholes, food is stuff.

Physical object

+O+U-D+R

Living being

+O+U-D+R

Legal agent

+L-U+D~R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide44

Entity-I-U-D+R

Analyze Roles

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

Agent

-I-U+D~R

  • ~R can’t subsume +R
  • Apple is not necessarily food. A poison-apple, e.g., is still an apple.
  • ~U can’t subsume +U
  • Caterpillars are wholes, food is stuff.

Physical object

+O+U-D+R

Living being

+O+U-D+R

Legal agent

+L-U+D~R

Food

+I-O~U+D~R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide45

Entity-I-U-D+R

Red

-I-U-D-R

Red apple

+I-O+U-D~R

Analyze Attributions

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

Agent

-I-U+D~R

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

Physical object

+O+U-D+R

Living being

+O+U-D+R

Legal agent

+L-U+D~R

Food

+I-O~U+D~R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide46

Entity-I-U-D+R

Red

-I-U-D-R

Red apple

+I-O+U-D~R

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

Agent

-I-U+D~R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Legal agent

+L-U+D~R

Food

+I-O~U+D~R

Social entity

-I+U-D+R

Fruit

+O+U-D+R

Animal

+O+U-D+R

Group of people

+I-O~U-D+R

Apple

+O+U-D+R

Lepidopteran

+O+U-D+R

Vertebrate

+I-O+U-D+R

Geographical

Region

+O-U-D+R

Country

+O+U-D+R

Caterpillar

+L+U-D~R

Butterfly

+L+U-D~R

Person

+O+U-D+R

Organization

+O+U-D+R

slide47

Entity-I-U-D+R

The backbone taxonomy

Amount of matter

+O~U-D+R

Location

+O-U-D+R

Group

+O~U-D+R

Physical object

+O+U-D+R

Living being

+O+U-D+R

Social entity

-I+U-D+R

Fruit

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slide48

Entity-I-U-D+R

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