NIST Foundations of Ontological Analysis Chris Welty, Vassar College.

NIST

Foundations of Ontological Analysis

Chris Welty, Vassar College

NIST

Part I

The Business Case

3NIST

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 community– McCarthy (1980) calls for “a list of things that exist”

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

knowledge engineering, etc.

4NIST

What is an Ontology?

complexity

a catalog

a set of generallogicalaxioms

a glossary

a set of text files a thesaurus

a collection of

taxonomies

a collection of frames

with automated reasoningwithout automated reasoning

5NIST

Why Ontology?

• “Semantic Interoperability”– Generalized database integration– Virtual Enterprises– e-commerce

• Information Retrieval– Surface techniques hit barrier– Query answering over document sets– Natural Language Processing

6NIST

Need more knowledge of what terms meanSame term, different concept

BookBook Manual

“The old man and the sea”

“Windows XP Service

Guide”

“The old man and the sea”

“Windows XP Service

Guide”

DB-DB-

Unintended models occur during integration

7NIST

Solution Knowledge

• DB- xy Book(x) author-of(y,x) Person(y) xy Manual(x) author-of(y,x) Company(y)

• Better captures intended meaning– Prevents (this) unintended model

• Allows better standardization

8NIST

Need more knowledge of what terms mean

Less expressive More expressive

Horse–Name–Age

Name: Top Hat/BillingsAge: 3

DB-DB-

The same object becomes two.

Horse–Name–Age–Owner

Name: Top HatOwner: BillingsAge: 3

9NIST

Solution Knowledge

• DB-– Identity Criteria: Same name

• DB-– Identity Criteria: Same name and owner

• Better captures intended meaning

10NIST

Need more knowledge about what the user wants“Can the user please be more specific?”

• Search for “Washington” (the person)– Google: 26,000,000 hits– 45th entry is the first relevant– Noise: places

• Search for “George Washington”– Google: 2,200,00 hits– 3rd entry is relevant– Noise: institutions, other people, places

11NIST

Solution Knowledge• Domain Knowledge

– Person• George Washington• George Washington Carver

– Place• Washington, D.C.

– Artifact• George Washington Bridge

– Organization• George Washington University

• Semantic Markup of question and corpora– What Washington are you talking about?

12NIST

Need more knowledge about the possible answers“Can the user please put more of the answer in the question?”

• Search for “Artificial Intelligence Research”

– Misses subfields of the general field– Misses references to “AI” and “Machine

Intelligence” (synonyms)– Noise: non-research pages, other fields, Mensa types

13NIST

Solution Knowledge• Domain Knowledge

– Sub-fields (of AI)• Knowledge Representation• Machine Vision etc. • Neural networks

– Synonyms (for AI)• Artificial Intelligence• Machine Intelligence

• Query Expansion– Add disjuncted “general terms” to search– Add disjuncted “synonyms” to search

• Semantic Markup of question and corpora– Add “general terms” (categories)– Add “synonyms”

14NIST

Need more knowledge of reasoningAllies of my enemies are my…?

• What are all the enemies of Iraq in the Persian Gulf according to the CIA World Fact Book?

– “Persian Gulf” appears as a region and a body of water.– Misses: allies of enemies– Noise: countries with interests in the Persian Gulf,

companies, ships, oil platforms

15NIST

Solution: Knowledge + Reasoning(Cycorp/SRI HPKB)

• Some axioms– Enemy of a country is a country– Ally of an enemy is an enemy– Enemy is reflexive– Countries are located in regions

• Reformulate (country

located-in . (region name = “Persian Gulf”) enemy . (country name = “Iraq”))

16NIST

Solution Theme: More KnowledgeOntologies - at least part of the solution

• “more semantics”, “richer knowledge” … ontologies• Idealized view

– Knowledge-enabled search engines act as virtual librarians• Determine what you “really mean”• Discover relevant sources• Find what you “really want”

– Knowledge-enabled web integrates standardized terms• Requires common knowledge on all ends

– Semantic linkage between questioning agent, answering agent and knowledge sources, etc.

• Hence the “Semantic Web”

17NIST

Key Challenges• Must build/design, analyze/evaluate, maintain/extend,

and integrate/reconcile ontologies

• Little guidance on how to do this– In spite of the pursuit of many syntactic standards– Where do we start when building an ontology?– What criteria do we use to evaluate ontologies?– How are ontologies extended?– How are different ontological choices reconciled?

• Ontological Modeling and Analysis– Does your model mean what you intend?– Will it produce the right answers?

18NIST

Most ontology efforts fail

• Why?– The quality of the ontology dictates its impact– Poor ontology, poor results– Ontologies are built by people

…The average IQ is 100

19NIST

Contributions• Methodology to help analyze & build consistent ontologies

– Formal foundation of ontological analysis– Meta-properties for analysis– “Upper Level” distinctions

• Standard set of upper-level concepts• Standardizing semantics of ontological relations

• Common ontological modeling pitfalls– Misuse of intended semantics

• Specific recent work focused on clarifying the subsumption (is-a, subclass) relation

20NIST

Upper LevelWhere do I start?

• Particulars– Concrete

• Location, event, object, substance, …– Abstract

• information, story, collection, …

• Universals– Property (Class)– Relation

• Subsumption (subclass), instantiation, constitution, composition (part)

21NIST

Subsumption• The most pervasive relationship in ontologies

– Influence of taxonomies and OO

• AKA: Is-a, a-kind-of, specialization-of, subclass (Brachman, 1983)– “horse is a mammal”

• Capitalizes on general knowledge– Helps deal with complexity, structure– Reduces requirement to acquire and represent redundant specifics

• What does it mean?

� x (x) (x)

Every instance of the subclass is necessarily an instance of the superclass

22NIST

Overloading Subsumption Common modeling pitfalls

• Instantiation• Constitution• Composition• Disjunction• Polysemy

23NIST

Instantiation (1)

T21

My ThinkPad (s# xx123)

ThinkPad Model

Ooops…

Question: What ThinkPad models do you sell?Answer should NOT include My ThinkPad -- nor yours.

Does this ontology mean that My ThinkPad is a ThinkPad Model?

24NIST

Instantiation (2)

T Series

My ThinkPad (s# xx123)

ThinkPad ModelNotebook Computer

model T 21

25NIST

Composition (1)

MemoryDisk Drive

Computer

Question: What Computers do you sell?Answer should NOT include Disk Drives or Memory.

Micro Drive

26NIST

Composition (2)

MemoryDisk Drive

Computer

Micro Drive

part-of

27NIST

Disjunction (1)

MemoryDisk Drive

Computer

Micro Drive

has-partComputer Part

Flashcard-110Camera-15has-part

Unintended model: flashcard-110 is a computer-part

28NIST

Disjunction (2)

Computerhas-part

Disk Drive Memory …

29NIST

Polysemy (1)(Mikrokosmos)

Abstract EntityPhysical Object

Book

Question: How many books do you have on Hemingway?Answer: 5,000

…..

30NIST

Polysemy (2)(WordNet)

Abstract EntityPhysical Object

BookSense 1

BookSense 2

….. Biography of Hemingway

31NIST

Constitution (1)(WordNet)

Amount of Matter

Physical Object

Entity

ComputerClayMetal

Question: What types of matter will conduct electricity?Answer should NOT include computers.

32NIST

Constitution (2)

Amount of Matter Physical Object

Entity

ComputerClayMetal

constituted

33NIST

Technical Conclusions• Subsumption is an overloaded relation

– Influence of OO – Force fit of simple taxonomic structures– Leads to misuse of is-a semantics

• Ontological Analysis– A collection of well-defined knowledge structuring relations– Methodology for their consistent application

• Meta-Properties for ontological relations• Provide basis for disciplined ontological analysis

34NIST

Applications of Methodology

• Ontologyworks• Ontoweb• TICCA, WedODE, Galen, …• Strong interest from and participation in

– Semantic web (w3c)– IEEE SUO– Wordnet– Lexical resources

NIST

Part II

Formalization

36NIST

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.

37NIST

Basic Philosophical Notions(taken from Formal Ontology)

• Identity– How are instances of a class distinguished from each

other• Unity

– How are all the parts of an instance isolated• Essence

– Can a property change over time• Dependence

– Can an entity exist without some others

38NIST

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.

39NIST

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

40NIST

Rigidity Constraint

+R ~R

• Why?

� x P(x) Q(x)

Q~R

P+R

O10

41NIST

Identity and Unity

• Identity: is this my dog?

• Unity: is the collar part of my dog?

42NIST

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’))

43NIST

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)

44NIST

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

45NIST

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)

46NIST

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

47NIST

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

48NIST

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)

49NIST

Unity Disjointness Constraint

Properties with incompatible UCs are disjoint+U ~U

50NIST

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

51NIST

Basic Property Kinds Table

O I R D

+ + + ± Type

- + + ± Quas -i type- + - - Mixin

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

- - ~ + Formalrole- - - - Attribution

52NIST

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)

53NIST

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

54NIST

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)

55NIST

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

56NIST

Phased Sortals

Backbone TaxonomyCategories

Top TypesTypes &Quasi-Types

FormalRoles

Material Roles

Attributions

Mixins

Non-sortals

Sortals

Idealized view of an ontology

NIST

Part III

Extended Example

58NIST

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

71NIST

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

72NIST

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

73NIST

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

74NIST

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

75NIST

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

76NIST

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

77NIST

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

78NIST

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)


79NIST

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)


80NIST

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)


85NIST

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!

86NIST

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!

87NIST

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

88NIST

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

89NIST

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

90NIST

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

91NIST

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

92NIST

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

93NIST

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

94NIST

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


95NIST

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

96NIST

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

97NIST

Use OntoClean for all your ontology cleaning needs!

98NIST

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

NIST Foundations of Ontological Analysis Chris Welty, Vassar College.

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Transcript of NIST Foundations of Ontological Analysis Chris Welty, Vassar College.