Conceptual Modeling and Ontological Analysis Nicola Guarino, LADSEB CNR,Italy Chris Welty, Vassar...

Conceptual Modeling and Ontological Analysis

Nicola Guarino, LADSEB CNR,ItalyChris 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)

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

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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

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Capturing Intended Meaning

• First order logic is ontologically neutral• Logical KBs often rely on natural language to

convey intended meaning

Red(x)

this apple is red

"purple" is a red

John is a red

Apple(x)this is an apple

this is apple

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Intended Models

An ontology consisting of just a vocabulary is of little use -

Unintended interpretations need to be excluded

Models M(L)

Intended models IK(L)

12

What is a conceptualization?

Conceptualization of scene 1:

<{a, b, c, d, e }, {on, above, clear, table }>

a

b

c e

d

Scene 1: blocks on a table

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What is a conceptualization?

The same conceptualization?

Scene 2: a different arrangement of blocks

a

b

c

e

d

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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.

apple

melasame conceptualization

LI

LE

15

Relations vs. Conceptual Relations

ordinary relations are defined on a domain D:

conceptual relations are defined on a domain space <D, W>

rn 2Dn

n : W 2Dn(Montague-style semantics)

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Ontologies constrain the intended meaning

Conceptualization C

Language LCommitment K=<C,>

Ontology

Models M(L)

Intended models IK(L)

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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

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Our Framework: Ontology-Driven

Conceptual Modeling

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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.

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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

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Framework

Formal Ontological Properties/Relations

Useful Property Kinds

Ontology-Driven Modeling Principles

Minimal Top-Level Ontology

User

Conceptualization Conceptual Model

OntologyOntology

Methodology

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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

A KB includes both

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Formal Ontological Analysis

• Mereology

• Identity, Unity, Essence

• Dependence

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Mereology

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Mereology• A possible primitive: proper part-of relation (PP)

– asymmetric– transitive– Pxy =def PPxy x=y

• Some further axioms:

Excluded models:

supplementation: PPxy z ( PPzy ¬ z=x)

principle of sum: z ( PPxz PPyz ¬ w(PPwz ¬ (Pwx Pwy)))

extensionality: x = y (Pwx Pwy)

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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

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Part, Constitution, and Identity

a + b

a b

Stack#1

Stack#1

b

aa b

a + b

• Structure may change identity

K

D

• Extensionality is lost• Constitution links the two entities• Constitution is asymmetric (implies dependence)

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Identity, Unity, Essence

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Framework





User


OntologyOntology

Methodology

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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…

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Identity and Unity

• Identity: is this my dog?

• Unity: is the collar part of my dog?

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Essence and rigidity

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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.

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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

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Identity and identity criteria

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Synchronic Identity Criteria

• Material objects: same-location• Immaterial objects: same-location not valid

any more...

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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

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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 can’t be defined.What we can have are just

informative constraints.

A priori identity?

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Identity criteria

• Based on the sameness of a certain property

(x,t) (y,t’) (((x,z,t) (y,z,t’)) x = y)

• t = t’ : synchronic; t ≠ t’ : diachronic

• Generalization:

(x,t) (y,t’) (x,y, t ,t’) x = y)

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Necessary ICs

A formula is a necessary IC for if

(x,t) (y,t’) x=y (x,y,t,t’)

… provided that:

• it is not equivalent to universal identity:¬xytt’ (x,y,t,t’) x=y

• it is not trivially true of all s:¬xytt’ (x,t) (y,t’) (x,y,t,t’)

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Sufficient ICs

A formula is a sufficient IC of if(x,t) (y,t’) (x,y,t,t’) x=y

… provided that:

• it is not equivalent to universal identity:¬xytt’ (x,y,t,t’) x=y

• itis not trivially false:xytt’ (x,y,t,t’)

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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

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Local Identity?

• Global IC: Rigid properties• Local IC (+L): non-Rigid properties• Local IC identifies instances of only when they are

instances of – 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)

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Unity and Unity Criteria

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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?

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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?

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Unity Conditions

• An object a is a whole under iff is an equivalence relation such that

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

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

can be seen as a generalized indirect connection

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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?

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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

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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)

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Disjointness Theorem

Properties with incompatible IC/UC are disjoint

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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

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Dependence

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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)

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Dependence Meta-Properties

• Our methodology currently uses only property dependence

• A property is dependent (+D) ifx(x) y 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.

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Using the meta-properties

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Framework





User


OntologyOntology

Methodology

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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

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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

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Exposing Unknown Differences

• Agreement:– An organization is a Social Entity

• Analysis:– Person 1: Social Entity +O+U+R -D– Person 2: Social Entity +O+U+R +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

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Property Kinds

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Framework





User


OntologyOntology

Methodology

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Basic Property kinds

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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)

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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

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Basic Property Kinds Table

O I R D+ + + Type- + + Quasi-type- + - - mixin- + ~ + Mat. role- + ~ - Phased sortal- - + Category- - ~ + Formal role- - - - Attribution

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Further Property Kinds:Common ICs/UCs

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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.

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Identity and unity conditions

Level Re-identificationSufficient Necessary

Unity

Atomic S/T continuity No proper parts

Static Same properties All entities of the domain

Mereological Same parts NO

Topological Maximal self-connectedness

Morphological Relative proximity

Functional Maximal functional self-connectedness

Biological Biological unity

Intentional Same intentional behaviour Single intentional behaviour

Social Same social behavior Maximal social self-connectedness

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Ontology-driven Modeling Principles

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Framework





User


OntologyOntology

Methodology

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Re-visiting abstraction relationships

• Taxonomic relationships (generalization)• Membership relationships (association)• Part-whole relationships (aggregation)

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Taxonomic relationships

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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

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Assumptions

• No entity without identity

• Every entity must instantiate a rigid property with identity (a type)

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Taxonomic Constraints

• +R ~R• -I +I• -U +U• +U ~U• -D +D

• Incompatible IC’s are disjoint

• Incompatible UC’s 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

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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 don’t affect identity

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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

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An extended example

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Framework





User


OntologyOntology

Methodology

82

Entity

Fruit

Physical objectGroup of people

Country

FoodAnimal Legal agent

Amount of matterGroup

Living being

LocationAgentRed

Red applePerson

Vertebrate

Apple

CaterpillarButterfly

Organization

Social entity

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Assign Meta-Properties

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Property AnalysisEntity, Location

• Entity– Everything is an entity– -I-U-D+R– Category

• Location– A generalized region of

space.– +O: by its parts

(mereologically extensional).

– ~U: no way to isolate a location

– -D+R– 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– -D+R– 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.– -D+R– Type

87

Property AnalysisPhysical Object, Living Being

• Physical Object– Isolated material

objects. – +O: same spatial

location (only synchronic, no common diachronic IC).

– +U: Topological– -D+R– Type

• Living Being– +O: same-DNA (only

nec.)– +U: biological unity– -D+R– Type

88

Property AnalysisFood, Animal

• Food– +I-O~U: amt. of matter– +D: something that eats

it.– ~R: being food is not

necessary...– Material Role

• Animal– +O: same-brain– +U: biological unity– -D+R– 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-O~U-D+R– Quasi-type

90

Property AnalysisSocial Entity, Organization

• Social Entity– A group of people

together for social reasons

– -I: no universal IC– +U: social-connection– -D+R– category

• Organization– A group of people

together, with roles that define some structure

– +O: same-mission and way of operating

– +U: functional– -D+R– 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– -D+R– Type

92

Property AnalysisApple, Red Apple

• Apple– +O: shape, color, skin

pattern (only nec)– +U: topological– -D+R– 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– -D+R– quasi-type

• Person– +O: same-fingerprint– +U: from animal– -D+R– 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

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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

97

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

98

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


• Living being is constituted of matter

99

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


• Physical object is constituted of matter

100

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


• Physical object is constituted of matter

101

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• 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

102

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• 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)


103

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)


104

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)


105

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• Same as for social entity. • Note also the same group

can constitute different organizations.

106

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• Same as for social entity. • Note also the same group

can constitute different organizations.

107

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



108

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 Phased Sortals

• 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.

Country+L+U-D~R

109

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




• There is an relationship between the two, but not subsumption.

Country+L+U-D~R

Geographical Region

+O-U-D+R

110

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 Caterpillar+L+U-D~R

Butterfly+L+U-D~R

• Caterpillar phases into butterfly - a true phased sortal

• There must be some property from which a single entity can uniquely claim identity across phases

• Define a rigid property which subsumes only the phases of the same entity.

Lepidopteran+O+U-D+R

111

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

• Try for a type, may be quasi.

• IC for Lepidopteran could be same-cocoon


112

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!

113

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!

114

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

115

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

116

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

117

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

118

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

119

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

120

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

121

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


122

Membership relationships

123

Framework





User


OntologyOntology

Methodology

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. Doesn’t pass the “is-a” test )

• Temporal instances– Beethoven isn’t 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





User


OntologyOntology

Methodology

130

A Minimal Top-level Ontology

EntityParticular

Concrete particularLocationObject

Abstract particularSetStructure…

UniversalProperty

Property Kinds...

Relation

131

Well-Founded Ontologies:Some 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)

Ontologists Wanted!

FOIS 2001Formal Ontology in Information Systems

Check out www.fois.org

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Conceptual Modeling and Ontological Analysis Nicola Guarino, LADSEB CNR,Italy Chris Welty, Vassar...

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