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Conceptual Modelling

An Introduction

(Module M2)

The 2013 International Conference on

Collaboration Technologies and

Systems

(CTS 2013)

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Module Layout

• Conceptual modelling for ontology building

– a key human activity

– Modeling and representation

– The nature of knowledge

– Syntax and semantics: from conceptual to

ontology modeling

– Static vs dynamic modeling (entity vs process)

– Key conceptual constructs (building bricks)

• Collaborative ontology building

• Languages, tools, and platforms

• And ... some practical exercises

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Perception and conceptualizion

• Objects cannot be seen … they appear as a sum of phenomena associated to them (a table? shapes, substance, color, weight, volume, …)

• Perception is an analytic activity (over individual phenomena) that is integrated afterward, to form the unity of the observed entity

• From the observation to the conceptualization

• Conceptualization: of entities, categories, relationships

• Abstraction: selection of relevant aspects, it is fundamental in modelling the reality (too complex)

• A Conceptual Model is a set of concepts well organized, on the base of principles independent of the domain

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Modeling is a key activity Modeling is a key activity to understand /

communicate a description of a given reality

• when the modeled objects do not exist yet (e.g., in designing a complex artifact),

• when the fragment of reality is not tangible (e.g., the organization of an enterprise),

• Concerns general (e.g., a mock-up of a building) or specific (e.g., the electric circuit schema) aspects

• Different models for the same complex entity (e.g., the human body)

• Objectives of modeling: understanding, communicating, exchanging information, predict behaviors and future situations (states)

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General Model Theory

Three pillars of a General Model Theory (Philosopher Herbert Stachowiak, 1973):

(1) Mimetism: Models are representative of “something”;

(2) Reductionism: Models are reductive in the sense that they depict some but not all aspects of the given fragment of reality;

(3) Pragmatism: Models are created for a purpose in the sense that a model is created at a given time, having a purpose in mind. Corollary: same reality at the same time may have different models

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Different modeling methods

• Concrete, e.g., a plastic model of a building

• Figurative, e.g., a drawing of a car, of a road

map

• Narrative, e.g., a text describing a landscape

• Schematic: schemes and diagrams that

illustrate the vectorial forces in the structure of

a bridge, the blue-print of an electric circuit

• Mathematical: e.g., a system of equations that

rigorously represents the air flowing in a wind

tunnel; a Boolean expression representing a

digital circuit

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Conceptual Model

Symbolic Modeling: describe the reality representing the relevant concepts and their relationships, starting from …

• concepts, expressed by means of terms (words) and symbols

– Figurative symbols: icons

– Mathematical symbols: letters, operators, …

– Diagrammatic symbols : boxes, ovals, arrows

Engineer tractor fixes

Language

• Needed to communicate, among people,

between people and computers

• Used to create Conceptual Models

• Natural Language: spoken by humans

• Artificial Language: conceived ad-hoc

Language, to create

• Sentences complex structures expressing

concepts, composed by

– Atomic elements: symbols and terminology

– Complex elements (... also sentences)

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Language - Syntax

• Symbols & Terms and composition rules for

sentences (i.e., complex structures)

engineer tractor fixes

engineer tractor fixes

Syntactically correct structure

Syntactically incorrect structure

Relation

Object

Actor

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Abstract Formal Syntax (sketch)

Unary Concept - uc: a (actor), o (object), p

(process)

Conceptual (binary) Relation: R

Conceptual Structure: cs

uc = a | o | p

cs = uc | cs R cs

Recursively, nested structures

cs = cs R (cs R2 cs)

Syntax - Example

uc1 = Engineer

uc2 = Tractor

R = fixes

(uc1 R uc2) (Engineer fixes Tractor)

The triple pattern: (Subject Rel Object)

Nested structures:

cs R (cs R2 cs) (Engineer fixes (Tractor ownedBy Father))

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engineer

tractor

fixes

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Language - Semantics

• Symbols and sentences (Syntactically correct )

• From the meaning of symbols & terms to the meaning of sentences

engineer tractor eats

engineer tractor fixes

engineer tractor blabla

What’s in a Concept?

Concept, is formed by

• Description (Intention)

– Purely descriptive, including its properties and

relationships

– If rigorous, it indicates necessary and sufficient

conditions

• Population (Extension)

– The collection of all individuals (instances) of the

concept

– Each individual needs to satisfy the intentional

description of the concept

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Formal Semantics (sketch)

Given a set of conceptual structures:

K = {csj}

Given a domain of interpetation:

D = {ei}

We define a semantic function S:

S : K 2D

{csi} {ei}

K D

S (Intentional level) (Extensional level)

Denotation

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(Engineer Fixes Tractor)

Engineer

Fixes Tractor

K = {csj}

D = {ei}

S

Denotation is compositional

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Standard FO Semantics

Semantics given by standard First Order

Interpetation theory: Interpretation domain DI Interpretation function I

Individuals

John

Mary

Concepts

Lawyer

Doctor

Vehicle

Relationships

hasChild

owns

(Lawyer AND Doctor) (by I. Horrocks)

Conceptual Modelling

Principles

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Synchronism vs Diachronism

• Static modelling (Synchronic)

– What we see when we take a picture

– Entities, Relationships, Properties

– Then, we automatically apply a

conceptualization process

– We recognise Categories, similarities and

differences, ... and we attach names to them

• Dynamic modelling (Diachronic)

– We understand how the reality: is evolving,

may further evolve, and we can influence it

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Conceptual Modeling

Static View

An exercise of conceptual modeling (static knowledge)

• Observe the reality, identify the relevant elements

• Create a schematic description by means of a suitable terminology and notation (conceptual model)

• Static Conceptual Modeling, includes Terms denoting: – Entities populating the observed reality

– Properties of entities (e.g., color, size, …), and

– Relationships among entities

A First Collaborative Conceptual Model

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A bedroom (V. VanGogh)

Exercise: Build a terminological model: entities, properties, relationships

(keep it, later we will ‘formalise’ the model)

A Collaborative Exercise

Your First Shared Conceptual Model

• Take pen ‘n paper

• Given a term, be ready to define a concept, by

using 140 characters: a Semantic Tweet

• Then, be ready to experience the rich diversity

of term interpretations

• Hence, we will collaborate and progressively

move towards a shared view of the concept

• Later, you will build a simplified ontology by

using

– SKOS and a N3 like formalization

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Conceptual Modeling Dynamic View

• Reality is continuously evolving

• Objects change state (position, form, color,

…) due to specific activities

• Activity: constructing, distroying, fixing,

traveling, cooking, washing, painting, …

• Identify, for each activity:

– Objects, that are modified / created / …

– Actors, that perform the activities

– Tools, used in performing the activities

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Modeling an activity

Trimming Sheep[f]

wool

Sheep[s]

scissors

Shepherd

With an intuitive diagramming notation

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Exemples of Dynamic

specification

Process: cooking – In: egg

– Actor: cook

– Out: omelet

Process: forging – In: steel

– Actor: blacksmith

– Out: gear

Process: designing – In: requirement, skills

– Actor: architect

– Out: design

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Symbolism in dynamic

representation

The great capacity of P. Bruegel (16th

cnetury) has been to organize in a single

scene almost 120 sayings drawn from the

popular wisdom that define a symbolic

universe: that of a reversed world.

Inspired by “Adagia”, a literary work of

Erasmus from Rotterdam

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Flamish sayings (Brugel)

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Some Flemish Sayings

• “Carring the light to the day with a

hamper” (losing time with useless

occupations) [49]

• “Filling up the well when the calf has

drowned” (repair a situation when is too

late) [57]

• “learning to bow to travel the world”

(you need to be flexible) [60]

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A systematic approach

Conceptual Modeling

Static Dimension

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Concepts and instances

Conceptual modeling refers (mainly) to concepts,

instances are modeled by data (numbers, strings, URIs).

With concept we mean a mental abstraction built (in

general) starting from the reality. A concept defines the

characteristics (properties) common to a set of coherent

objects.

With instance we mean any element of the extension of a

concept. It is an individual object with identity, described

by its relevant characteristics (i.e., all its properties are

evaluated).

In understanding the reality, the first primary notions

are: concepts and instances

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Conceptualization

Classification

Conceptualization & Instantiation

DOG animal

that barks ------

Fido ------ ------

Instance Descr.

individual

concept

Symbolic Concept Descr. Mental world

Real world

Digital world

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Semiotics Theory of Signs

• In linguistic theories (Semiotics) – Relation between symbols (of the language) and concepts

(denotation)

• In formal theories – Relation between concepts models and instances (instatiation)

• The ontological-semiotic closure (C. K. Ogden triangle1)

Symbol

Concept

Instance (Referent)

(1The Meaning of Meaning: A Study of the Influence of Language upon Thought and

the Science of Symbolism, 1923)

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The pipe (Surrealiste painter René.Magritte)

[this is NOT a pipe]

Ontology Building Key Conceptual Constructs

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Building a Concept

Conceptual modeling aims at creating a description of a fragment of realty, through the definition of some concepts, with their correlations

A concept (entity): defined by using a terminological expression:

• Label (concept name) – Person

• Properties – Name, age, address (attributes – dataProperties)

– Friends, company (associations – references)

• Relations with other concepts – Married (symmetrical)

john married mary mary married john)

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Entities and Relationships

• Entities (Concepts)

– Tangible: Student, Person, Cat, Bike, Chair

– Intangible: Course, Film, Sale, Story

– Abstract: Natural number, Algorithm,

Philosophy, Luck

• Relations (conceptual)

– Follows(Student,Course)

– Owner(Person,Bike)

– xxx(Person,Student)

– yyy(Bike,Weel)

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Attributes - Associations

Cat:

• Name, Age, Owner

Person:

• Name, Age, Phone, FCode, Weight

Student:

• Name, Age, Phone, FC, Weight,

University, Faculty, AverageMark

Attribute: printable data

Association: entity-id (reference)

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Conceptual Kinds

OPAL – Object, Process, Actor modeling Language

• Object

– Passive entity, whose state may change by means of the effect of a process

• Actor

– Active entity, capable of performing a process

• Process

– Activities performed by actors, aimed at modifying entities

(a kind may depends on the situation)

Conceptual Relations

• O, P, A are unary concepts (= entities)

• They specify what exist in a given

(fragment of the) reality

• The next step is to define their mutual

relationships: binary, n-ary relations

We have:

• Universal relations: they are valid in any

possible observable domain

• Domain specific relations: make sense

only in specific contexts

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Universal Relation:

Refinement

• It is a vertical relation

• Associate a concept to a more refined one

that is:

– Better specified,

– Enriched in its description

Two golden hierarchical relations

• Specialization: IsA

• Decomposition: PartOf

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Specialization

• Given a concept, refine its description

• Increase the precision of the description

• More precise classification of individuals

• Produces a Taxonomy

Ex.

Student IsA Person;

Teenager IsA Person

• Inverse

Generalization 40

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Specialization

Given a concept, it is specialized by applying rigorous mechanisms:

• Extension: introducing additional properties

– Student extends person, with university, faculty, avergeMark

• Restriction: restrincting the range (i.e., legal values) of one or more properties

– Teenager restrincts person on age (with values between 13 and 19)

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Attributes & Associations

• Cat: Name, Age, Owner

• Person: Name, Age, Phone, FC, Weight

• Student: Name, Age, Phone, FC, Weight,

University, Faculty, AverageMark

N

A P

FC

W

U

F

AM

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Taxonomy (ISA)

Vehicle

Public Vehicle

Plane Train Bike Car

Private Vehicle

Example: The IsA hierarchy of Vehicle

Key feature of a Taxonomy: property inheritance

(in case with restricted range)

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Inheritance (of properties)

name

age

Faculty

AvarageMark

name

age

(strict inheritance)

Person

Student

ISA

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Decomposition/Aggregation (Mereology)

• Theory of parthood relations (Plato:

Stanford Encyclopedia of Philosophy)

• Also indicated as Part/Whole relation

• It is an important ontological relation,

since it is applicable both to instances

and concepts (but... hard to axiomatize)

• Inheritance: characteristics of relevant

parts are transmitted to the whole

– Color: body car

– Power: engine car

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Decomposition / Aggregation

(PartOf )

Vehicle

Engine

Piston Carburetor Hood Door

Body

PartOf is transitive

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Building hierarchical structures

A hierarchy of concepts can be built in two ways:

- Top-down, when the less refined concepts are first

identified and then more refined concepts are progressively

identified

- Bottom-up, when you start identifying the most refined

concepts, and then you group them under more general

ones.

Hierarchies can be applied both to entities (objects, actors),

activities (processes, tasks, actions), and relationships

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Universal Relation

Predication • Identifies (HasA) the concepts that denote the

relevant charateristics of an entity: properties

• Associate the properties to the entities

Concepts Attributes

C1 C2

C3

a4

a5

a3 a9

a9

a1

a8

Ex. Person: name, age, address(street, nr, postCode, city), tel

Invoice: nr, date, {item (lineNr, descr, cost, qty, lineTot) }, total

Universal Relation

Instantiation

On the ‘double nature’ of a concept:

• Intentional definition: a collection of

properties and constraints (e.g., a dog

has: name, owner, )

• Extensional definition: a set of instances

that satisfy the intentional definition (e.g., a

dog includes: fido, pluto, rex, ...)

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Concepts - Instances

Instantiation

Person Student

Cat

ed

mary

miao

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Relation between Concepts and Instances

Concepts Instances

Persons

Students

denotes

denotes

containment

Person

Student

ISA

Other Universial Relations

• Membership, when a composite structure includes

a set of elements of the same kind (e.g.,

tennisPlayers in a tennisClub)

• Containment, among two composite structures,

when one includes the other (left-handed

TennisPlayers)

• Similarity, with a similarity degree k (typically:

k = 0 .. 1)

• Causality: a causes b (b isCausedBy a)

• Precedence (temporal): a precedes b (b follows a),

strict / loose

• Proximity (spatial): a proxTo b (symmetric) 52

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Universal Relations Summary

• Generalization /Specialization (ISA) – Student ISA Person (A)

– Car ISA Vehicle (O)

– Frying ISA Cooking (P)

• Part/Whole (PartOf) – Tail PartOf Dog

– Weel PartOf Car

– Seasoning PartOf Cooking

• Predication (HasA) – Person HasA Name

– Car HasA Color

– Hoven HasA Temperature

• Similarity (SIM/k) – Bird SIM/0.5 Airplane

– Pear SIM/0.7 Apple

– Tennis SIM/0.7 Squash

• Instantiation (InstOf) – Pluto InstanceOf Dog

– MyAlfa InstanceOf Car

– TodayDinner InstanceOf Dining

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Domain-dependent relations

• Defined between 2 (binary) or more (n-ary) concepts

• Unlike Universal Relations, they assume a meaning in a specific application domain

• Relations valid both at concept and instance level

– Frame hanging_on Wall

– Invoice issued_by provider

– Student attends Couse [john attends informationSystems]

Conclusions

• Ontology engineering relies on

Conceptual Modeling principles

• Conceptualization is a basic human

activity, but here we need to make it explicit

and systematic

• An ontology

– is a socio-technical artefact, that needs a

collaboration practice for its construction and

evolution

– reflects a shared perception of an application

domain

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