Ontological Analysis of Taxonomic Relationships

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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
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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.

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Dealing withOntological Relativism

• Deciding about the meta-properties carried by a
  given property
• Is up to YOU!
• But a common agreement must be achieved about the
  formal meaning (and practical utility) of
  meta-properties

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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)

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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
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Basic Philosophical Notions(taken from Formal
Ontology)

• Essence
• Identity
• Unity
• Dependence

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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.

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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

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Rigidity Constraint

• R ? R
• Why?
• ?x P(x) ? Q(x)

QR
PR
O10
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Identity and Unity

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

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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))

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A Stronger NotionGlobal ICs

• Local ICf(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)

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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

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Identity meta-properties

• Supplying (global) identity (O)
• Having some own IC that doesnt hold for a
  subsuming property
• Carrying (global) identity (I)
• Having an IC (either own or inherited)
• Not carrying (global) identity (-I)

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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

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Unity Criteria

• An object x is 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

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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)

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Unity Disjointness Constraint
Properties with incompatible UCs are disjoint
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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

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Basic Property Kinds Table
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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)

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A formal ontology of properties
Category R
Non-sortal -I
Attribution -R-D
Role RD
Formal Role
Property
Material role
Anti-rigid R
Non-rigid -R
Phased sortal -D L
Mixin -D
SortalI
Type O
Rigid R
Quasi-type -O
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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)

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Taxonomic Constraints

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

• Incompatible ICs are disjoint
• Incompatible UCs are disjoint

• Categories subsume everything
• Roles cant subsume types

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An extended example
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Dealing withOntological Relativism

• Deciding about the meta-properties carried by a
  given property
• Is up to YOU!
• But a common agreement must be achieved about the
  formal meaning (and practical utility) of
  meta-properties

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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

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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

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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

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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

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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

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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

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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

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Property AnalysisFruit

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

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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

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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

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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

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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

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Entity
assign meta-properties
Social entity
Organization
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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
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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
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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
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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
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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
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Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• 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 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
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Entity-I-U-DR
Analyze taxonomic links
Amount of matter OU-DR
Location O-U-DR

• 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 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
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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
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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
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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
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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
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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 a 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
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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
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Entity-I-U-DR
Analyze Phased Sortals
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
Caterpillar LU-DR
Butterfly LU-DR
Organization OU-DR
Person OU-DR
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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