2. 2
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
3. 3
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
4. 4
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)
5. 5
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
6. 6
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
7. 7
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 tractorfixes
8. 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) 8
9. 9
Language - Syntax
• Symbols & Terms and composition rules for
sentences (i.e., complex structures)
engineer tractorfixes
engineer tractor
fixes
Syntactically correct structure
Syntactically incorrect structure
Relation
Object
Actor
10. 10
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)
11. 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)) 11
engineer
tractor
fixes
12. 12
Language - Semantics
• Symbols and sentences (Syntactically
correct )
• From the meaning of symbols & terms to
the meaning of sentences
engineer tractoreats
engineertractor fixes
engineer tractorblabla
13. 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
13
14. 14
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)
16. 16
Standard FO Semantics
Semantics given by standard First Order
Interpetation theory:
Interpretation domain DIInterpretation function I
Individuals
John
Mary
Concepts
Lawyer
Doctor
Vehicle
Relationships
hasChild
owns
(Lawyer AND Doctor)(by I. Horrocks)
18. 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
18
19. 19
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
20. 20
A bedroom (V. VanGogh)
Exercise: Build a terminological model: entities, properties, relationships
(keep it, later we will ‘formalise’ the model)
21. 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
21
22. 22
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
25. 25
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
27. 27
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]
29. 29
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
31. 31
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)
34. 34
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)
35. 35
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)
37. 37
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)
38. 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 38
39. 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
39
40. 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
41. 41
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)
42. 42
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
43. 43
Taxonomy (ISA)
Vehicle
Public Vehicle
Plane TrainBikeCar
Private Vehicle
Example: The IsA hierarchy of Vehicle
Key feature of a Taxonomy: property inheritance
(in case with restricted range)
45. 45
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
47. 47
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
48. 48
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
49. 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, ...)
49
51. 51
Relation between Concepts and
Instances
Concepts Instances
Persons
Students
denotes
denotes
containment
Person
Student
ISA
52. 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
53. 53
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
54. 54
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]
55. 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 55
