Evaluating Ontological Decisions with OntoClean Chris Welty, Vassar College, USA Nicola Guarino, LADSEB-CNR, Italy

Evaluating Ontological Decisions with OntoClean

Chris Welty, Vassar College, USANicola Guarino, LADSEB-CNR, Italy

2

What is Ontology?

• A discipline of Philosophy– Meta-physics dates back to Artistotle– Ontology dates back to 17th century– The science of what is

• Borrowed by AI– McCarthy calls for “a list of things that exist”

• Evolution of meaning– Now refers to domain modelling, conceptual

modeling, knowledge engineering, etc.

3

What is an Ontology?

complexity

a catalog

a set of generallogical

constraintsa glossary

a set of text files a thesaurus

a collection of

taxonomies

a collection of frames

with automated reasoningwithout automated reasoning

4

OntoClean 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.

5

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

6

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 (x) (x)

7

Ontology-driven conceptual modeling

Formal Ontological Properties/Relations

Useful Property Kinds

Ontology-Driven Modeling Principles

Minimal Top-Level Ontology

User

Conceptualization Conceptual Model

OntologyOntology

Methodology

8

Basic Philosophical Notions(taken from Formal Ontology)

• Essence

• Identity

• Unity

• Dependence

9

Essence and Rigidity

• Certain entities have essential properties.– Hammers must be hard.– John must be a person.

• Certain properties are essential to all their instances (compare being a person with being hard).

• These properties are rigid - if an entity is ever an instance of a rigid property, it must always be.

10

Formal Rigidity is rigid (+R): x (x) � (x)

– e.g. Person, Apple

is non-rigid (-R): x (x) ¬ � (x)– e.g. Red, Male

is anti-rigid (~R): x (x) ¬ � (x)– e.g. Student, Agent

11

Rigidity Constraint

+R ~R

• Why?

� x P(x) Q(x)

Q~R

P+R

O10

12

Identity and Unity

• Identity: is this my dog?

• Unity: is the collar part of my dog?

13

Identity criteria

• Classical formulation:

(x) (y) ((x,y) x = y)

• Generalization:(x,t) (y,t’) ((x,y,t,t’) x = y)

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

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

(x,y, t ,t’) = z ((x,z,t) (y,z,t’))

14

A Stronger Notion:Global ICs

• Local IC:

(x,t) (y,t’) ((x,y,t,t’) x = y)

• Global IC (rigid properties only):

(x,t) ((y,t’) (x,y,t,t’) x = y)

15

Identity Conditions along Taxonomies

• Adding ICs:– Polygon: same edges, same angles

• Triangle: two edges, one angle– Equilateral triangle: one edge

• Just inheriting ICs:– Person

• Student

16

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)

17

Identity Disjointness Constraint

Properties with incompatible ICs are disjoint

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

Examples:• sets vs. ordered sets• amounts of matter vs. assemblies

18

Unity Criteria

• An object x is a whole under iff is an equivalence relation that binds together all the parts of x, such that

P(y,x) (P(z,x) y,z))but not

y,z) x(P(y,x) P(z,x))

• P is the part-of relation can be seen as a generalized indirect connection

19

Unity Meta-Properties

• If all instances of a property are wholes under the same relationcarries unity (+U)

• When at least one instance of is not a whole, or when two instances of are wholes under different relations, does not carry unity (-U)

• When no instance of is a whole, carries anti-unity (~U)

20

Unity Disjointness Constraint

Properties with incompatible UCs are disjoint+U ~U

21

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

22

Basic Property Kinds Table

O I R D

+ + + ± Type

- + + ± Quas -i type- + - - Mixin

- + ~ + Mat.role- + ~ - Phasedsortal- - + ± Category

- - ~ + Formalrole- - - - Attribution

23

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)

24

A formal ontology of properties

Property

Non-sortal-I

Role~R+D

Sortal+I

Formal Role

Attribution -R-D

Category +R

Mixin -D

Type +O

Quasi-type -O

Non-rigid-R

Rigid+R

Material roleAnti-rigid~R Phased sortal -D +L

25

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)

26

Taxonomic Constraints

• +R ~R• -I +I• -U +U• +U ~U• -D +D

• Incompatible IC’s are disjoint

• Incompatible UC’s are disjoint

• Categories subsume everything

• Roles can’t subsume types

27

Phased Sortals

Backbone TaxonomyCategories

Top TypesTypes &Quasi-Types

FormalRoles

Material Roles

Attributions

Mixins

Non-sortals

Sortals

Idealized view of an ontology

28

An extended example

29

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

42

Entity

Fruit

Physical objectGroup of people

Country

FoodAnimal Legal agent

Amount of matterGroup

Living being

LocationAgentRed

Red applePerson

Vertebrate

Apple

CaterpillarButterfly

Organization

Social entity

assign meta-properties

43

Remove non-rigid propertiesEntity-I-U-D+R

Physical object+O+U-D+R

Amount of matter +O~U-D+R Group

+O~U-D+R

Organization+O+U-D+R

Location+O-U-D+R

Living being+O+U-D+R

Person+O+U-D+R

Animal+O+U-D+R

Social entity-I+U-D+R

Agent-I-U+D~R

Apple+O+U-D+R

Fruit+O+U-D+R

Food+I-O~U+D~R

Country+L+U-D~R

Legal agent+L-U+D~R

Group of people+I-O~U-D+R

Red apple+I-O+U-D~R

Red-I-U-D-R

Vertebrate+I-O+U-D+R

Caterpillar+L+U-D~R

Butterfly+L+U-D~R

44

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze taxonomic links

• ~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

45

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+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

46

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+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

47

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+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

48

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+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

49

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+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)


50

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+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)


51

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+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)


56

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Roles

Geographical Region

+O-U-D+R Caterpillar+L+U-D~R

Butterfly+L+U-D~R

Lepidopteran+O+U-D+R

Agent-I-U+D~R

• ~R can’t subsume +R• Really want a type

restriction: all agents are animals or social entities.

• Subsumption is not disjunction!

57

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Roles

Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

• ~R can’t subsume +R• Really want a type

restriction: all agents are animals or social entities.

• Subsumption is not disjunction!

58

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Roles

Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

• ~R can’t subsume +R• Another disjunction: all

legal agents are countries, persons, or organizations Legal agent

+L-U+D~R

59

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Roles

Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

• ~R can’t subsume +R• Another disjunction: all

legal agents are countries, persons, or organizations Legal agent

+L-U+D~R

60

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Roles

Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

Legal agent+L-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.

Food+I-O~U+D~R

61

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Roles

Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

Legal agent+L-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.

Food+I-O~U+D~R

62

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Attributions

Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

Legal agent+L-U+D~R

• No violations• Attributions are

discouraged, can be confusing.

• Often better to use attribute values (i.e. Apple Color red)

Food+I-O~U+D~R

Red-I-U-D-R

Red apple+I-O+U-D~R

63

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

Legal agent+L-U+D~R

Food+I-O~U+D~R

Red-I-U-D-R

Red apple+I-O+U-D~R

64

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Geographical Region

+O-U-D+R


The backbone taxonomy

65

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Agent-I-U+D~R

Apple+O+U-D+R

Fruit+O+U-D+R

Food+I-O~U+D~R

Legal agent+L-U+D~R


Red apple+I-O+U-D~R

Red-I-U-D-R


Caterpillar+L+U-D~R

Butterfly+L+U-D~R

Country+O+U-D+R

Geographical Region

+O-U-D+R


66

Entity

Fruit

Physical objectGroup of people

Country

FoodAnimal Legal agent

Amount of matterGroup

Living being

LocationAgentRed

Red applePerson

Vertebrate

Apple

CaterpillarButterfly

Organization

Social entity

Before

67

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Agent-I-U+D~R

Apple+O+U-D+R

Fruit+O+U-D+R

Food+I-O~U+D~R

Legal agent+L-U+D~R


Red apple+I-O+U-D~R

Red-I-U-D-R


Caterpillar+L+U-D~R

Butterfly+L+U-D~R

Country+O+U-D+R

Geographical Region

+O-U-D+R


After

68

Use OntoClean for all your ontology cleaning needs!

Documents

Evaluating Ontological Decisions with OntoClean Chris Welty, Vassar College, USA Nicola Guarino, LADSEB-CNR, Italy