Ph d course on formal ontology and conceptual modeling

Formal Ontology and Conceptual Modeling
Nicola Guarino
National Research Council, Institute for Cognitive Science and
Technologies (ISTC-CNR)
Laboratory for Applied Ontology (LOA)
www.loa.istc.cnr.it

Course Objectives and Contents
• Basic tools of formal ontological analysis and their practical role
in conceptual modelling and knowledge representation.
• Notion of "ontological level" and need for ontologically non-
neutral representation formalisms.
• Fundamentals of formal ontology: parts, essence and identity,
unity and plurality, dependence, properties and qualities...
• ...as powerful "tools" to make explicit hidden assumptions
behind information systems, in order to improve semantic
interoperability and cognitive transparency.
• OntoClean and DOLCE as examples of such general tools.
• OntoClean: methodology for analysing ontological implications
of taxonomic relationships
• DOLCE: upper ontology based on carefully designed distinctions
among objects, events, and qualities.
• Ontology-driven conceptual modeling: discussion of common
conceptual modeling problems, using concrete examples mainly
taken from e-government and enterprise modeling applications.

Why this course
Conceptual modeling is the activity of formally
describing some aspects of the physical and social
world around us for the purposes of understanding
and communication
(John Mylopoulos)

4
Applied Ontology:
an emerging interdisciplinary area
• Applied Ontology builds on philosophy, cognitive science, linguistics
and logic with the purpose of understanding, clarifying, making explicit
and communicating people's assumptions about the nature and
structure of the world.
• This orientation towards helping people understanding each other
distinguishes applied ontology from philosophical ontology, and
motivates its unavoidable interdisciplinary nature.
ontological analysis: study of
content as such
(independently of representation)

7
Kinds of knowledge
Fido is black
Fido is black or Fido is not black
If Jack is a bachelor, then he is not married
synthetic
logical
analytic
terminological
(assertional)
Terminological knowledge is about
relationships between terms and concepts

15
Do we know what to REpresent?
• First analysis,
• THEN representation…
Unfortunately, this is not the current practice…
• AI researchers have focused more on the nature of reasoning
than in the nature of the real world
Essential ontological promiscuity of AI: any agent creates its
own ontology based on its usefulness for the task at hand
(Genesereth and Nilsson 1987)
No representation without
conceptual and ontological analysis!

7
The problem: subtle distinctions in meaning
The e-commerce case:
“Trying to engage with too many partners too fast is one of the main reasons
that so many online market makers have foundered.
The transactions they had viewed as simple and routine
actually involved many
subtle distinctions in terminology and meaning”
Harvard Business Review, October 2001

9
Subtle distinctions in meaning...
• What is an application to a public administration?
• What is a service?
• What is a working place?
• What is an unemployed person?

4
The focus of ontological analysis:
from form to CONTENT
! The key problems
• content-based information access (semantic matching)
• content-based information integration (semantic integration)
• To approach them, content must be studied, understood, analyzed as
such, independently of the way it is represented.
• Traditionally, computer technologies are not really good for that...
ontological analysis: study of
content qua content
(independently of representation)

18
Signs and their content
• Sign kinds in Peirce:
• icon: analogic association with content
• indexes: causal association
• symbols: conventional assotiation

19
Signs and concepts
• Episodic memory vs. semantic memory:
• we memorize both speciﬁc facts and general concepts
• But what is a concept?
• What does it mean to represent it?

20
The triangle of meaning - 1
“Cat”
Cat
this cat (or these cats) here...

21
Sign
Concept
Referent

22
Intension ed extension
• Intension (concept): part of meaning corresponding to general
principles, rules to be used to determine reference (typically,
abstractions from experience)
• Extension (object): part of meaning corresponding to the
effective reference
• Only by means of the concept associated to the sign “cat” we
can correctly interpret this sign in various situations
• The sign’s referent is the result of this interpretation
• Such interpretation is a situated intentional act

23
Again on intension and extension
• Concepts with zero extension
• square circle, unicorn (different cases!)
• Concepts with same extension and different intension
• equilateral triangle and equiangular triangle
• president of Council of Ministers and president of Milan (deﬁnite
descriptions)
• morning star and evening star

24
“Berlusconi”
Berlusconi
this person here

The FRISCO tethraedron
Actor
(Observer)
Conception
Domain (referent) Representation
Actor
(Observer)
Conception
Domain (referent) Representation
E. Falkenberg, W. Hesse, P. Lindgreen, B.E. Nilsson, J.L.H. Oei, C. Rolland, R.K. Stamper,
F.J.M. Van Assche, A.A. Verrijn-Stuart, K. Voss: FRISCO - A Framework of Information
System Concepts - The FRISCO Report. IFIP WG 8.1 Task Group FRISCO. Web version:
http://www.mathematik.uni-marburg.de/~hesse/ papers/fri-full.pdf (1998)

26
Example 1: the concept of red

26
...assuming a constant conceptual domain
a b {b}
{}
{a,b}
{a}a b
a b
a b

27
Example 2: the concept of on
b
a
{<a,b >}
a
b
{<b,a >}
ab {}

32
Representing Concepts as intensional relations
Intensional relations are defined on a domain space <D, W>
r n
∈ 2
D
n
ρn : W→ 2
Dn
(Carnap, Montague)
ordinary (extensional) relations are defined on a domain D:
But what are possible worlds?
What are the elements of a conceptual domain?
r2 ⊆ D ⋅ D rn ⊆ Dnr1 ⊆ D

28
Concepts, properties, and relations:
terminology issues
• Non-relational concepts are often called properties
• Relational concepts are often called relations
• ...but properties and relations can be understood as intensional
or extensional... Concepts are always intensional!!
• We also assume that properties are always intensional.
• To stress the difference between intensional and extensional
relations, we shall call the former conceptual relations

3. Concepts and Conceptualizations

30
What is a conceptualization? A cognitive approach
• Humans isolate relevant invariances from physical reality (quality distributions) on the basis
of:
• Perception (as resulting from evolution)
• Cognition and cultural experience (driven by actual needs)
• (Language)
• presentation: atomic event corresponding to the perception of an external phenomenon
occurring in a certain region of space (the presentation space).
• Presentation pattern (or input pattern): a pattern of atomic stimuli each associated to an
atomic region of the presentation space. (Each presentation tessellates its presentation space
in a sum of atomic regions, depending on the granularity of the sensory system).
• Each atomic stimulus consists of a bundle of sensory quality values (qualia) related to an
atomic region of timespace (e.g., there is red, here; it is soft and white, here).
• Domain elements corresponds to invariants within and across presentation patterns

31
From experience to conceptualization
Conceptualization C
(relevant invariants across
situations: D, ℜ)
State of
affairs
State of
affairsPresentations
D : cognitive domain
ℜ : set of conceptual relations on elements of D

33
Possible worlds as presentation patterns
(or sensory states)
Presentation pattern: unique (maximal) pattern of qualia ascribed to a spatiotemporal
region tessellated at a certain granularity
...This corresponds to the notion of state for a sensory system (maximal combination of
values for sensory variables)
Possible worlds are (for our purposes)
sensory states
(or if you prefer, [maximal] sensory situations)

PhD course on Foundations of Knowledge Representation and Ontological Analysis, Trento, May 2008 31
What is a conceptualization
• Formal structure of (a piece of) reality as perceived and organized by an
agent, independently of:
• the vocabulary used
• the actual occurence of a speciﬁc situation
• Different situations involving same objects, described by different
vocabularies, may share the same conceptualization.
apple
mela
same conceptualization
LI
LE

Logic is neutral about content
...but very useful to describe the formal structure (i.e.,
the invariances) of content

Ontologies and ontological analysis: an introduction - FOIS 2008, Saarbrücken, October 31st, 2008 4
Kinds of knowledge
Fido is black
Fido is black or Fido is not black
If Jack is a bachelor, then he is not married
synthetic
logical
analytic
terminological
(assertional)
Terminological knowledge is about
relationships between terms and concepts

Ontological commitment
• Every natural language (or maybe every contextualized sentence) commits to some
ontology (i.e., makes assumptions on what there is), in two ways:
• Through a closed system of grammatical features
• Through an open system of lexemes
• "Ontological semantics" [Nirenburg & Raskin 2004]: the semantics is driven by an ontology.
• Practical role of ontologies for NLP systems
• Every organization, every computer system
• Adopts a certain lexicon, to which an intended semantics is ascribed.
• Makes (implicit) ontologic assumptions

What kinds of commitment?
• Commitment to individuals:
• Quine: every (logical) theory commits to the class of entities it quantifies on.
• Problems:
• Does everything we refer to exist?
– Questionable entities: Events, features, qualities, fictional characters...
• Should different linguistic behaviors mark/reflect different ontological categories?
• Commitment to concepts:
• Problem: how are the things we refer to organized in categories? How to capture the
classification rules of such categories? How to capture the similarities among
individuals belonging to a single category (meaning postulates)?
• Ontologies are a way to specify both commitments.

19PhD course on foundations of concptual modelling and ontological analysis, Trento, May 2009
Signs and concepts
• Episodic memory vs. semantic memory:
• we memorize both speciﬁc facts and general concepts
• But what is a concept?
• What does it mean to represent it?

“Cat”
Cat
this cat (or these cats) here...

Sign
Concept
Referent

Intension ed extension
• Intension (concept): part of meaning corresponding to general
principles, rules to be used to determine reference (typically,
abstractions from experience)
• Extension (object): part of meaning corresponding to the
effective reference
• Only by means of the concept associated to the sign “cat” we
can correctly interpret this sign in various situations
• The sign’s referent is the result of this interpretation
• Such interpretation is a situated intentional act

26
Example 1: the concept of red
{b}
{a}
{a,b}
{}
ba
a b
a b
a b

Example 2: the concept of on
b
a
{<a,b >}
a
b
{<b,a >}
ab {}

32
Representing Concepts as intensional relations
Intensional relations are defined on a domain space <D, W>
r n
∈ 2
D
n
ρn : W→ 2
Dn
(Carnap, Montague)
ordinary (extensional) relations are defined on a domain D:
But what are possible worlds?
What are the elements of a domain of discourse?
r2 ⊆ D ⋅ D rn ⊆ Dnr1 ⊆ D

30PhD course on foundations of conceptual modelling and ontological analysis, Trento, October 2010
• Humans isolate relevant invariances from physical reality (quality distributions) on the basis
of:
• (Language)
• presentation: atomic event corresponding to the perception of an external phenomenon
occurring in a certain region of space (the presentation space).
• Presentation pattern (or input pattern): a pattern of atomic stimuli each associated to an
atomic region of the presentation space. (Each presentation tessellates its presentation space
in a sum of atomic regions, depending on the granularity of the sensory system).
• Each atomic stimulus consists of a bundle of sensory quality values (qualia) related to an
atomic region of timespace (e.g., there is red, here; it is soft and white, here).

31PhD course on foundations of conceptual modelling and ontological analysis, Trento, October 2010
Conceptualization C
situations: D, ℜ)
State of
affairs
State of

apple
mela
LI
LE

28
Concepts, properties, and relations:
terminology issues
• Non-relational concepts are often called properties
• Relational concepts are often called relations
• ...but properties and relations can be understood as intensional
or extensional... Concepts are always intensional!!
• We also assume that properties are always intensional.
• To stress the difference between intensional and extensional
relations, we shall call the former conceptual relations
•

SEMINÁRIO DE PESQUISA EM ONTOLOGIA NO BRASIL - UFF - IACS - Departamento de Ciência da Informação - Niterói, 11-12/8/200
23
Philosophical ontologies
• Ontology: the philosophical discipline
• Study of what there is (being qua being...)
...a liberal reinterpretation for computer science:
content qua content, independently of the way it is represented
• Study of the nature and structure of “reality”
• A (philosophical) ontology: a structured system of entities assumed to exists,
organized in categories and relations.

SEMINÁRIO DE PESQUISA EM ONTOLOGIA NO BRASIL - UFF - IACS - Departamento de Ciência da Informação - Niterói, 11-12/8/200
Computational ontologies
24
Speciﬁc (theoretical or computational) artifacts
expressing the intended meaning of a vocabulary
in terms of primitive categories and relations describing
the nature and structure of a domain of discourse
Gruber: “Explicit and formal speciﬁcations of a conceptualization”
...in order to account for the competent use of vocabulary in real situations!
Computational ontologies, in the way they evolved, unavoidably mix
together philosophical, cognitive, and linguistic aspects.
Ignoring this intrinsic interdisciplinary nature
makes them almost useless.

apple
mela
LI
LE

• Humans isolate relevant invariances from physical reality (quality distributions) on
the basis of:
• (Language)
• presentation: atomic event corresponding to the perception of an external
phenomenon occurring in a certain region of space (the presentation space).
• Presentation pattern (or input pattern): a pattern of atomic stimuli each associated
to an atomic region of the presentation space. (Each presentation tessellates its
presentation space in a sum of atomic regions, depending on the granularity of the
sensory system).
• Each atomic stimulus consists of a bundle of sensory quality values (qualia) related
to an atomic region of timespace (e.g., there is red, here; it is soft and white, here).

Conceptualization C
situations: D, ℜ)
State of
affairs
State of

The basic ingredients of a conceptualization
(simpliﬁed view)
• cognitive objects (and events): mappings from (sequences of) presentation patterns
into their parts
• for every presentation, such parts constitute the perceptual reiﬁcation of
the object.
• multiple objects in a single presentation: equivalence relationship among
parts based on unity criteria
• concepts and conceptual relations: functions from (sequences of)
presentation patterns into sets of (tuples of) cognitive objects
• if the value of such function (the concept’s extension) is not an empty set,
the correponding perceptual state is a (positive) example of the given
concept
• Rigid concepts: same extension for all presentation patterns (possible worlds)

Ontology
Language L
Intended
models for
each IK(L)
Ontological commitment K
(selects D’⊂D and ℜ’⊂ℜ)
Interpretations
I
Ontology models
Models MD’(L)
Bad
Ontology
~Good
relevant invariants
across presentation
patterns:
D, ℜ
Conceptualization
State of
affairs
State of
affairs
Presentation
patterns
Perception Reality
Phenomena

Ontology Quality: Precision and Correctness
Low precision, max correctness
Less good
Low precision, low correctness
WORSE
High precision, max correctness
Good
Max precision, low correctness
BAD

Levels of Ontological Precision
Ontological precision
Axiomatic
theory
Glossary
Thesaurus
Taxonomy
DB/OO
scheme
tennis
football
game
ﬁeld game
court game
athletic game
outdoor game
game
athletic game
court game
tennis
outdoor game
ﬁeld game
football
game
NT athletic game
NT court game
RT court
NT tennis
RT double fault
game(x) → activity(x)
athletic game(x) → game(x)
court game(x) ↔ athletic game(x) ∧ ∃y. played_in(x,y) ∧ court(y)
tennis(x) → court game(x)
double fault(x) → fault(x) ∧ ∃y. part_of(x,y) ∧ tennis(y)
Catalog

Why ontological precision is important

33
All
interpretations
of “apple”
Why ontological precision is important
Area
of false
agreement!
B - Juice
producer’s
intended
interpretations
A - Apple
producer’s
intended
interepretations
Interpretations
allowed by B’s
ontology
Interpretations
allowed by A’s
ontology

When precision is not enough
Only one binary predicate in the language: on
Only three blocks in the domain: a, b, c.
Axioms (for all x,y,z):
on(x,y) -> ¬on(y,x)
on(x,y) -> ¬∃z (on(x,z) ∧ on(z,y))
Non-intended models are excluded, but the rules for
the competent usage of on in different situations are
not captured.
Excluded conceptualizations
a
c
b
a
Indistinguishable conceptualizations
a
c
a
c
a
c
a
c

Database A: keeping track of fruit stock
36
Variety Quantity
Granny Smith 12
Golden delicious 10
Stark delicious 15

Database B: keeping track of juice stock
37
Variety Quantity
Granny Smith 12
Golden delicious 10
Stark delicious 15

The reasons for ontology inaccuracy
• In general, a single intended model may not discriminate between
positive and negative examples because of a mismatch between:
• Cognitive domain and domain of discourse: lack of entities
• Conceptual relations and ontology relations: lack of primitives
• Capturing all intended models is not sufﬁcient for a “perfect” ontology
! ! Precision: non-intended models are excluded
! ! Accuracy: negative examples are excluded

When is a precise and accurate ontology useful?
1. When subtle distinctions are important
2. When recognizing disagreement is important
3. When general abstractions are important
4. When careful explanation and justiﬁcation of ontological commitment
is important
5. When mutual understanding is more important than interoperability.

Kinds of ontology change
(to be suitably encoded in versioning systems!)
• Reality changes
• Observed phenomena
• Perception system changes
• Observed qualities (different qualia)
• Space/time granularity
• Quality space granularity
• Conceptualization changes
• Changes in cognitive domain
• Changes in conceptual relations
• metaproperties like rigidity contribute to characterize them (OntoClean assumptions reﬂect a particular
conceptualization)
• Logical characterization changes
• Domain
• Vocabulary
• Axiomatization (Correctness and Precision)
• Accuracy

Ontologies vs. classiﬁcations
• Classiﬁcations focus on:
• access, based on pre-determined criteria
(encoded by syntactic keys)
• Ontologies focus on:
• Meaning of terms
• Nature and structure of a domain

42
A simple classiﬁcation
Pictures
Home Work Vacations
Italy Europe
What’s the meaning of these terms?
What’s the meaning of arcs?

Ontologies vs. Knowledge Bases
• Knowledge base
• Assertional component
• reﬂects speciﬁc (epistemic) states of affairs
• designed for problem-solving
• Terminological component (ontology)
• independent of particular states of affairs
• Designed to support terminological services
Ontological formulas are (assumed to be)
invariant, necessary information

The two fundamental scenarios for semantic
integration
1. Same domain, same terminology, same conceptualization: e.g,
different processes within a very small, family-managed
enterprise (everybody does everything)
2. Same domain, shared terminology, different conceptualization:
e.g., different branches of a big company with a strong
organization structure..
Current ontologies have been born for 2, but, they are actually
used for 1: just shared data schemes. The result is the so-
called “data sylos” effect.

45
Role of ontologies in information architecture
! ! ! ! ! (thanks to Dagobert Soergel)
• Relate concepts to terms. Clarify their meaning by providing a
system of definitions.
• Provide a semantic road map and common conceptual reference
tool across different disciplines, languages, and cultures
• Make medical concepts clear to social science researchers and vice versa…
• Improve communication. Support learning by helping the learner
ask the right questions
• Support information retrieval and analysis
• Support the compilation and use of statistics
• Support meaningful, well-structured display of information.
• Support multilinguality and automated language processing
• Support reasoning.

A single, imperialistic ontology?
• An ontology is ﬁrst of all for understanding each other
• ...among people, ﬁrst of all!
• not necessarily for thinking in the same way
• A single ontology for multiple applications is not necessary
• Different applications using different ontologies can co-exist and co-
operate (not necessarily inter-operate)
• ...if linked (and compared) together by means of a general enough
basic categories and relations (primitives).
• If basic assumptions are not made explicit, any imposed, common
ontology risks to be
• seriously mis-used or misunderstood
• opaque with respect to other ontologies

2
The formal tools of ontological analysis
• Theory of Parts (Mereology)
• Theory of Unity and Plurality
• Theory of Essence and Identity
• Theory of Dependence
• Theory of Composition and Constitution
• Theory of Properties and Qualities
The basis for a common ontology
vocabulary
Idea of Chris Welty, IBM Watson Research
Centre, while visiting our lab in 2000

3
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)
• Why formal?
• Two meanings: rigorous and general
• Formal logic: connections between truths - neutral wrt truth
• Formal ontology: connections between things - neutral wrt reality
• NOTE: “represented in a formal language” is not enough for
being formal in the above sense!
• (Analytic ontology may be a better term to avoid this confusion)

4
The ﬁrst steps of ontological analysis
Language L
Conceptualization C
situations: D, ℜ)
State of
affairs
State of
affairsSituations
Ontological commitment K
(selects D’⊂D and ℜ’⊂ℜ)
• Be clear about the domain of discourse (existence...)
• Choose the relevant concepts and conceptual relations
• Choose the primive relations
• Choose meaningful names for these

5
Mereology: an example of
formal ontological analysis
• Primitive: proper part-of relation (PP)
• asymmetric
• transitive
• Useful deﬁnitions:
• Pxy =def PPxy ∨ x=y
• Oxy =def ∃ z(Pzx ∧ Pzy)
• Axioms:
Excluded models:
(weak) supplementation: PPxy → ∃z (Pzy ∧ ¬ Ozx)
principle of sum: ∃z ∀w (Owz ↔ (Owx ∨ Owy ))
extensionality: x = y ↔ ∀w(Pwx ↔ Pwy)
?

Weak and strong supplementation
• weak supplementation: PPxy → ∃z (Pzy ∧ ¬ Ozx)
• strong supplementation: ¬ Pxy → ∃z (Pzy ∧ ¬ Ozx)
• Strong supplementation implies extensionality.
6

A Violation of Supplementation Axiom
7
Dov Dory, Words from pictures for
dual-channel processing,
Communications of the ACM 51,
2008

8
Part, Constitution, and Identity
a + b
a b
Castle#1
A castle
b
aa b
Two
blocks
• Parts not enough to make the whole: structure
creates a new entity
K
D
• Mereological extensionality is lost
• Constitution links the two entities
• Constitution is asymmetric (implies dependence)

9
Mereological sums
• A bad choice:
• x + y =df ιz∀w(Pzw ↔ (Pxw ∧ Pyw))
• A good choice:
• x + y =df ιz∀w(Owz ↔ (Owx ∨ Owy))

10
Sets vs. mereological sums
• What’s the difference between {a} and a?
• What is {}?
• If {a,b} ∈ S, does a S?
• Sets of concrete things are abstract
• Sums of concrete things are concrete!

Parthood and Connection
• A new primitive: topological connection
• C(x,y)
• Axioms:
• C(x,x)
• C(x,y) -> C(y,x)
• Parthood deﬁned in terms of connection:
• P(x,y) =def ∀z (C(z,x) -> C(z,y))
• Unfortunately this only works if the domain is restricted to
regions of space:
• Counterexamples:
• The boat in the lake
• The ﬂy in the glass
• ...
11

2
Kinds, roles, attributions
rock
igneous rock sedimentary rock
metamorphic rock
large rock grey rock
large grey igneous rock
grey
sedimentary
rock
pet metamorphic rock
[From Brachman, R ., R. F ikes, et al. 1983. “Krypton: A Functional Approach to
Knowledge Representation”, IEEE Computer]
How many rock kinds are there?

3
The answer
• According to Brachman & Fikes 83:
• It’s a dangerous question, only “safe” queries about analytical
relationships between terms should be asked
• In a previous paper by Brachman and Levesque on terminological
competence in knowledge representation [AAAI 82]:
• “an enhancement mode transistor (which is a kind of transistor) should be
understood as different from a pass transistor (which is a role a transistor
plays in a larger circuit)”
• These issues have been simply given up while striving for logical
simpliﬁcation and computational tractability
• The OntoClean methodology, based on formal ontological analysis,
allows us to conclude: there are 3 kinds of rocks (appearing in the
ﬁgure)

4
From the logical level to the ontological level
• Logical level (no structure, no constrained meaning)
• ∃x (Apple(x) ∧ Red(x))
• Epistemological level (structure, no constrained meaning):
• ∃x:apple Red(x) (many-sorted logics)
• ∃x:red Apple(x)
• a is a Apple with Color=red (description logics)
• a is a Red with Shape=apple
• Ontological level (structure, constrained meaning)
• Some structuring choices are excluded because of ontological
constraints: Apple carries an identiy condition, Red does not.
Ontology helps building “meaningful” representations

5
The source of all problems:
(slightly) different meanings for words
• A (simple-minded) painter may intepret the words “Apple” and “Red” in a completely
different way:
• Three different reds on my palette: Orange, Appple, Cherry
• So an expression like ∃x:red Apple(x) may mean that there is an “Apple” red.
• Two different ontological assumptions behind the Red predicate:
• adjectival interpretation: being a red thing doesn’t carry an identity criterion
(uncountable)
• nominal interpretation: being a red color does carry an identity criterion (countable)
Formal ontological distinctions help making
intended meaning explicit
Ontological analysis can be deﬁned as the process of eliciting and discovering relevant
distinctions and relationships bound to the very nature of the entities involved in a
certain domain, for the practical purpose of disambiguating terms having different
interpretations in different contexts.

The Ontological Level
(Guarino 94)
Level Primitives Interpretation Main feature
Logical Predicates,
functions
Arbitrary Formalization
Epistemological Structuring
relations
Arbitrary Structure
Ontological Ontological
relations
Constrained
(meaning postulate s )
Meaning
Conceptual Conceptual
relations
Subjective Conceptualization
Linguistic Linguistic
terms
Subjective Language
dependence

Terminological competence - kinds of
relations
• Woods’ “What’s in a link?” (1975):
JOHN
! HEIGHT: 6 FEET
! KISSED: MARY
• "no longer do the link names stand for attributes of a node, but rather
arbitrary relations between the node and other nodes”
• different notations should be used

8
Kinds of attributes
JOHN
! HEIGHT: 6 FEET
! RIGHT-LEG: LEG#1
! MOTHER: JANE
! KISSED: MARY
intrinsic quality
part
role
external relation
We need different primitives to express different structuring relationships among concepts
We need to represent non-structuring relationships separately
Current description logics tend to collapse EVERYTHING!

2
Essential properties
• For an individual
• John must have a brain
• John must be a human
• John must be alive
• For a type
• All human beings must have a brain
• All human beings must be “a whole” (all of a piece)

3
Unity and Essence
• Unity: is the collar part of my
dog?
• Being a whole is often a (very
relevant) essential property
• Dogs are essential wholes...

4
Deﬁning unity
• A tentative formulation: x is a whole under a unifying relation U iff U is an
equivalence relation that binds together all the parts of x, such that,
necessarily,
P(y,x) → (P(z,x) ↔ U(y,z))
but not
U(y,z) ↔ ∃x(P(y,x) ∧ P(z,x))
• P is the part-of relation
• U can be seen as a generalized indirect connection

5
Kinds of Whole
• Depending on the nature of the unifying relation, we can distinguish:
• Topological wholes (a piece of coal, a heap of coal)
• Morphological wholes (a constellation)
• Functional wholes (a hammer, a bikini)
• Social wholes (a population)
* a whole can have parts that are themselves wholes (with a different
unifying relation)

Essential wholes vs. contingent wholes
• Consider the amount of matter that constitues a castle.
• At every time it constitutes the castle, it is contingently a whole.
• It is not necessarily a whole.
• The castle is necessarily a whole, the amount of matter it is
constituted is a whole only contingently.
6

7
Unity Reﬁned
Problem: the unity relation may not link together all the parts (think of a family as a whole)
δU(x) =df U(x, x) (x belongs to the domain of U)
UU(x)=df ΣδU
(x)∧∀y,z((δU(y)∧δU(z)∧P(y, x)∧ P(z, x)) ➝ U(y, z))
(x is unified by U)
WU(x) =df MaxUU
(x) (x is a whole under U)
Σφ(x)=df ∀y(P(y, x) ➝ ∃z(φ(z) ∧ P(z, x) ∧O(z, y)) (sum of φs)

8
Unity and Plurality
• Ordinary objects: wholes or sums of wholes
• Singular: no wholes as proper parts
• Plural: sums of wholes
• Plural wholes (the sum is also a whole)
• Collections (the sum is not a whole)

A note on pluralities: Instances vs. members
• Often we use the same names for classes and their characteristic properties
• John is a member of “Person” ↔ Person(John)
• Tree#1 is a member of “TheBlackForest” ↔ TheBlackForest(Tree1) ??
• violates usual intended interpretation of unary predicates: property
shared by all instances of the corresponding class.
• doesn’t pass is-a test
• Membership is a relation between individuals
9

Rigidity and Identity
www.loa-cnr.it

11
Essential properties and rigidity
• Certain entities must have some properties in order to exist
• John must have a brain
• John must be a person.
• Certain properties are essential to all their instances
(being a person vs. being hard).
• These properties are rigid - Their extension is the same in all possible
worlds. If an entity is ever an instance of a rigid property, it must
necessarily be such.
• By the way, what’s the meaning of exist?
• Being an element of the domain of discourse
• Being present at a certain time (or in a certain world...)

12
Formal Rigidity
• φ is rigid (+R):! ∀x (◊φ(x) → !φ(x))
• e.g. Person, Apple
• φ is non-rigid (-R):! ∃ x (◊φ(x) ∧ ¬ !φ(x))
• e.g. Red, Male
• φ is anti-rigid (~R):! ∀ x (◊φ(x) → ¬ !φ(x)) e.g. Student, Agent
Meta-properties

13
Formal rigidity - variations
• Takint actual existence into account:
!∀x( φ(x) → !(E(x) → φ(x)) )
• Taking time and actual existence into account:
!∀xt( (E(x,t)∧ φ(x,t)) → !∀t'(E(x,t') → φ(x)))
• Welty, C. and Andersen, W. Towards OntoClean 2.0: A framework for rigidity
(Applied Ontology 1(1), 2006)

14
Identity criteria
• Classic formulation:
φ(x) ∧ φ(y) → (ρ(x,y) ↔ x = y)
(φ carries the identity criterion ρ)
• Generalization:
φ(x,t) ∧ φ(y,t’) → (Γ(x,y,t,t’) ↔ x = y)
(synchronic: t = t’; diachronic: t ≠ t’)
• In most cases, Γ is based on the sameness of certain characteristic features:
Γ(x,y,t,t’) = ∀z (χ(x,z,t) ∧ χ(y,z,t’))
• Non-triviality condition:
• Γ( x,y, t, t’) must not contain an identity statement between x and y!

15Ontologies and ontological analysis: an introduction - FOIS 2008, Saarbrücken, October 31st, 2008
From identity criteria to weak identity conditions
• Finding necessary and sufﬁcient ICs for a given property may be very hard.
• In most cases, to apply the OntoClean methodology it is enough to detect
whether a certain property P carries supplementary membership conditions (in
addition to those logically implied by P itself)
• A property P carries an identity condition C if all its instances necessarily
satisfy C, and C is not logically implied by P
• Typical example: having some essential parts or qualities

16
Sortals and other properties
• Sortals (horse, triangle, amount of matter, person, student...)
• Carry identity conditions
• Usually correspond to nouns
• High organizational utility
• Non-sortals (red, big, old, decomposable, dependent...)
• No identity
• Usually correspond to adjectives
• Span across different sortals
• Limited organizational utility (but high semantic value)

What about our rocks?
• Igneous rock, metamorphic rock, sedimentary rock
do supply identity conditions.
• Large rock, grey rock, pet rock
DO NOT!
• Not all properties are the same...

Carrying vs. Supplying Identity
• Supplying identity (+O)
• Carrying an IC (or relevant essential property) that doesn’t hold for all directly
subsuming properties
• Carrying identity (+I)
• Not supplying identity, while being subsumed by a property that does.
• Common sortal principle: x=y -> there is a common sortal supplying their identity
• Theorem: only rigid properties supply identity

Identity, Countability, and Mass Nouns
• Nouns vs. adjectives
• Countability implies identity
• The problem with mass nouns: does the viceversa hold?
• Being [an amount of] water:
• Uncountable if arbitrarily divisible (but still carries identity!)
• Countable if we assume molecules
– We do have criteria for distinguishing and counting water molecules
– We do have criteria for distinguishing and counting sums of water molecules
– [compare with “being a group of people”]
• Being made of water:
• if x and y are made of water, nothing helps us to decide whether they are identical or not
• So, “Being an amount of water” is a sortal,”Being made of water” is not.

Identity Disjointness Constraint
Properties with incompatible ICs are disjoint
ICs impose constraints on sortals, making their ontological
nature explicit:
Examples:
• countries vs. geographical regions
• passengers vs. persons
• assemblies vs. amounts of matter
• sets vs. ordered sets

Ontologies and ontological analysis: an introduction - FOIS 2008, Saarbrücken, October 31st, 2008
Unity as a special case of identity condition
21
Properties with incompatible unity conditions
are disjoint
Unity-related metaproperties for a property P:
• +U: all instances of P have a common unity criterion
• ~U: no instance of P has a unity criterion
• -U: some instances of P have a unity criterion

Why bother with this?
• Formal ontological analysis requires analyzing all properties according to their
meta-properties – This is a lot of work!
• Why perform this analysis?
• Makes modeling assumptions clear, which:
• Helps resolving known conﬂicts
• Helps recognizing unkown conﬂicts
• Imposes constraints on standard modeling primitives (generalization,
aggregation, association)
• Elicits natural distinctions
• …results in more reusable ontologies

Resolving Ontological Conﬂicts
• Two well-known linguistic ontologies deﬁne:
• Physical Object is-a Amount of Matter (WordNet)
• Amount of Matter is-a Physical Object (Pangloss)
• Amount of Matter
• unstructured /scattered “stuff”
• Identity: mereologically extensional
• Unity: intrinsically none (anti-unity)
• Physical Object
• Isolated material body
• Identity - three options:
• None
• Non-extensional
• Extensional
• Unity: Topological
Conclusion: the two concepts are disjoint. Physical objects
are constituted by amounts of matter

• +R ⊄ ~R
• -I ⊄ +I
• -U ⊄ +U
• +U ⊄ ~U
• Incompatible ICʼs are disjoint
• Incompatible UCʼs are disjoint
Ontologies and ontological analysis: an introduction - FOIS 2008, Saarbrücken, October 31st, 2008
Taxonomic constraints
24

Example - Identity
• Is time-interval a subclass of time-duration?
• Initial answer: yes
• IC for time-duration
• Same-length
• IC for time-interval
• Same start & end time-duration
time-interval
?

The case of “Nation”
Group
Group of peopleSocial group
Nation1 Nation2 Nation3
Admin. district
Region
Location
Object
depends on is located inconstituted by

PhD course on conceptual modeling and ontological analysis
How ontological levels
simplify taxonomies
social-event
mental-event
physical-event
communication-event
perceptual-event
social-event
mental-event
physical-event
communication-event
perceptual-event

3
Taxonomic Constraints
• +R ⊄ ~R
• -I ⊄ +I
• -U ⊄ +U
• +U ⊄ ~U
• -D ⊄ +D
• Incompatible IC’s are disjoint
• Incompatible UC’s are
disjoint

Entity
Fruit
Physical object
Group of people
Country
Food
Animal
Legal agent
Amount of matter
Group
Living being
Location
AgentRed
Red apple
Person
Vertebrate
Apple
Caterpillar
Butterﬂy
Organization
Social entity
assign meta-properties

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

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-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

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
• Physical objects can change parts and
remain the same, but amounts of
matter can not (incompatible ICs)
• Physical object is constituted of matter

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
• Physical objects can change parts and
remain the same, but amounts of matter
can not (incompatible ICs)
• Physical object is constituted of matter

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
• Meta-properties ﬁne
• Identity-check fails: being alive is a
contingent property for physical
objects, and an essential property
for animals
• Constitution again

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-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)

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
• A group can’t change parts - it becomes a
different group
• A social entity can change parts - it’s more
than just a group (incompatible IC)

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Analyze non-rigid properties
Agent
-I-U+D~R
• ~R can’t subsume +R
• Subsumption is not disjunction!

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Agent
-I-U+D~R
• Another disjunction: all legal agents are persons or
organizations
Legal agent
+L-U+D~R

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Caterpillar
+L+U-D~R
Butterﬂy
+L+U-D~R
Agent
-I-U+D~R
Legal agent
+L-U+D~R
• Apple is not necessarily food. A poison-apple,
e.g., is still an apple.
• Caterpillars are wholes, food is stuff.
Food
+I-O~U+D~R

Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Country
+L+U-D~R Caterpillar
+L+U-D~R
Butterﬂy
+L+U-D~R
Food
+I-O~U+D~R
• Identity check: a location can’t change parts…
• 2 senses of country: geographical region and political entity.
• Split the two senses into two concepts, both rigid, both types.

Country
+O+U-D+R
Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Country
+L+U-D~R
Geographical
Region
+O-U-D+R Caterpillar
+L+U-D~R
Butterﬂy
+L+U-D~R
Food
+I-O~U+D~R
There is a relationship between the two,
but not subsumption.
Agent
-I-U+D~R
Legal agent
+L-U+D~R

Food
+I-O~U+D~R
Country
+O+U-D+R
Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Look for missing types
Geographical
Region
+L+U-D~R
Butterﬂy
+L+U-D~R
Lepidopteran
+O+U-D+R
Agent
-I-U+D~R
Legal agent
+L-U+D~R
• Caterpillars and butterﬂies cannot be
vertebrate
• There must a rigid property that subsumes the
two, supplying identity across temporary
phases

Country
+O+U-D+R
Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Look for missing types
Geographical
Region
+L+U-D~R
Butterﬂy
+L+U-D~R
Lepidopteran
+O+U-D+R
Agent
-I-U+D~R
Legal agent
+L-U+D~R
Food
+I-O~U+D~R

Country
+O+U-D+R
Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Analyze Attributions
Geographical
Region
+L+U-D~R
Butterﬂy
+L+U-D~R
Lepidopteran
+O+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

Country
+O+U-D+R
Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Geographical
Region
+L+U-D~R
Butterﬂy
+L+U-D~R
Lepidopteran
+O+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

Country
+O+U-D+R
Entity-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
Apple
+O+U-D+R
Fruit
+O+U-D+R
Group of people
+I-O~U-D+R
Vertebrate
+I-O+U-D+R
Geographical
Region
+O-U-D+R
Lepidopteran
+O+U-D+R
The backbone taxonomy

Entity-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
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
Country
+O+U-D+R
Geographical
Region
+O-U-D+R
Lepidopteran
+O+U-D+R

Entity
Fruit
Physical
object Group of people
Country
Food
Animal Legal agent
Amount of matter
Group
Living being
Location
AgentRed
Red apple
Person
Vertebrate
Apple
Caterpillar
Butterﬂy
Organization
Social entity
Before

Entity-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
Legal agent
+L-U+D~R
Group of people
+I-O~U-D+R
Red apple
+I-O+U-D~R
Vertebrate
+I-O+U-D+R
Caterpillar
+L+U-D~R
Butterﬂy
+L+U-D~R
Country
+O+U-D+R
Geographical
Region
+O-U-D+R
Lepidopteran
+O+U-D+R
After

Websters’ Int. Dictionary on roles
2
•!a character assigned to or assumed by someone
•!a socially prescribed pattern of behaviour corresponding to
an individual’s status in a particular society
•!a part played by an actor
•!a function performed by someone or something in a
particular situation, process, or operation.

3
Roles are properties
• Basic Idea (Sowa 2000)
Roles can be ‘predicated’ of different entities, i.e., different
entities can play the same role
• Standard representation
Roles are represented, in FOL, as unary predicates whose
instances are their players:
• Student(john) -> John plays the Student role

4
Sortal specialization
• Type specialization (e.g. Living being → Person)
• New features (especially essential properties) affect identity
• ICs are 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

5
Roles are ‘dynamic’ and ‘antirigid’
! Basic Idea (Steimann 2000): Roles have temporal/modal relations with their
players
• An entity can play different roles simultaneously
• In 2003, B. was the Italian Prime Minister, the President of the European
Union, the president of the Forza Italia party, the owner of the Mediaset
company, an Italian citizen, a defendant at a legal trial.
• An entity can cease playing a role (antirigidity)
• In 1960, B. was a piano bar singer, now he is the IPM.
• An entity can play the same role several times, simultaneously
• In 2003, B. had two presidencies / was president twice.
• A role can be played by different entities, simultaneously or at different
times
• Today, there are 4319 Italian National Research Council researchers.
• In 2000, the Italian Prime Minister was D., now it is B.

6
Roles have a relational nature
• Basic Idea (Sowa, Guarino&Welty)
Roles imply patterns of relationships, i.e., they depend—via
these patterns—on additional ‘external’ properties
• Which kind of dependence?

7
Dependence
• Between particulars
• Existential dependence (specific/generic) (also constant dependence)
• Hole/host, person/brain, person/heart
• Internal vs. external dependence
• Region/boundary....
• Historical dependence
• Person/parent
• Causal dependence
• Heat/fire
• Between universals
• Definitional dependence
• P depends on Q iff Q is involved in the definition of P [Fine 1995].
• External definitional dependence [Masolo et al. 2004]: +D/-D

9
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 role
Anti-rigid
~R Phased sortal -D

10
Types, Roles, and disjointness
Organism
Person Plant
*Child *Student

11
What's the right model?
Customer
Person Organization Customer
Person Organization
a b

12
The solution [Guizzardi 2005]
«FormalRole»
Customer
«role»
PrivateCustomer
«role»
CorporateCustomer
«Type»
Person
Organization
«Type»

13
The dual nature of roles [Masolo et al 2004]
• Basic Idea (Sowa 2000)
Roles can be ‘predicated’ of different entities, i.e., different
entities can play the same role
• Standard representation
Roles as properties
• Social (and dynamic) aspects of roles not accounted for
• Roles are created and disappear; are deﬁned by conventions; are
adopted and accepted by communities of agents
• Roles need to be considered both as properties (also called role
properties) and “ﬁrst-class citizens” (simply called roles, typically
focusing on socially-constructed roles).

Dolce: motivating its
ontological distinctions

2
DOLCE
a Descriptive Ontology for Linguistic and Cognitive Engineering
• Strong cognitive/linguistic bias:
• descriptive (as opposite to prescriptive) attitude
• Categories mirror cognition, common sense, and the lexical structure of natural language.
• Emphasis on cognitive invariants
• Categories as conceptual containers: no “deep” metaphysical implications
• Focus on design rationale to allow easy comparison with different ontological
options
• Rigorous, systematic, interdisciplinary approach
• Rich axiomatization
• 37 basic categories
• 7 basic relations
• 80 axioms, 100 deﬁnitions, 20 theorems
• Rigorous quality criteria
• Documentation

3
Explaining the Descriptive Approach
• Descriptive: semantic structure of sentences is preserved (as best as possible)
• Revisionary: ontological eliminativism based on paraphrasability:
• John gives a kiss to Mary (Mary is given a kiss by John)
• John kisses Mary (Mary is kissed by John)
• John gives a ﬂower to Mary
• *John ﬂowers Mary
• There is a hole in this wall
• This wall is holed
• This statue has a long nose
• This statue is long-nosed

4
The traps of revisionism
• Is systematic paraphrasing really possible (also for complex
sentences)?
• There are 7 holes in this piece of cheese
• How to choose whether paraphrasing?
• Mary makes a leap
• Mary makes a cake
• Can we account for proper inferences?
• There are two things John gave to Mary: a kiss and a ﬂower
• Where to stop while eliminating entities?
• Should we paraphrase everything in terms of bunches of molecules moving
around?...

5
The rich ontology of natural language
Multiple co-located events
• John sings while taking a shower
Multiple co-located objects
• I am talking here
• *This bunch of molecules is talking
• *What’s here now is talking
• This statue is looking at me
• *This piece of marble is looking at me
• This statue has a strange nose
• *This piece of marble has a strange nose
Individual qualities
- The nurse measured the patient’s temperature
- I like the color of this rose
- The color of this rose turned from red to brown in one week

6
DOLCE’s basic taxonomy
Object (endurant)
! Physical
! ! Amount of matter
! ! Physical object
! ! Feature
! Non-Physical
! ! Mental object
! ! Social object
! …
Event (perdurant)
! Static
! ! State
! ! Process
! Dynamic
! ! Achievement
! ! Accomplishment
Quality
! Physical
! ! Spatial location
! ! …
! Temporal
! ! Temporal location
! ! …
! Abstract
Abstract
! Quality region
! ! Time region
! ! Space region
! ! Color region
! ! …
! …

7
DOLCE taxonomy
Q
Quality
PQ
Physical
Quality
AQ
Abstract
Quality
TQ
Temporal
Quality
PD
Perdurant
EV
Event
STV
Stative
ACH
Achievement
ACC
Accomplishment
ST
State
PRO
Process
PT
Particular
R
Region
PR
Physical
Region
AR
Abstract
Region
TR
Temporal
Region
T
Time
Interval
S
Space
Region
AB
Abstract
SetFact…
… … …
TL
Temporal
Location
SL
Spatial
Location
… … …
ASO
Agentive
Social Object
NASO
Non-agentive
Social Object
SC
Society
MOB
Mental Object
SOB
Social Object
F
Feature
POB
Physical
Object
NPOB
Non-physical
Object
PED
Physical
Endurant
NPED
Non-physical
Endurant
ED
Endurant
SAG
Social Agent
APO
Agentive
Physical
Object
NAPO
Non-agentive
Physical
Object
…
AS
Arbitrary
Sum
M
Amount of
Matter
… … … …

8
DOLCE's Basic Ontological Choices
• Objects (aka continuants or endurants) and Events (aka occurrences or
perdurants)
• distinct categories connected by the relation of participation.
• Qualities
• Individual entities inhering in Objects or Events
• can live/change with the objects they inhere in
• Instance of quality kinds, each associated to a Quality Space representing
the "values" (qualia) that qualities (of that kind) can assume. Quality Spaces
are neither in time nor in space.
• Multiplicative approach
• Different Objects/Events can be spatio-temporally co-localized: the relation
of constitution is considered.

Some cognitive distinctions between objects
and events (just intuitions!)
• Objects are recognized, events are just perceived
• Perceptions of events accumulate in time
• Perceptions of objects superpose each other in time
9

10
Objects and Events
• Objects (3D continuants)
• Need a time-indexed parthood relation
• Exist in time
• Can genuinely change in time
• May have non-essential parts
• All proper parts are present whenever they are present (wholly presence, no
temporal parts)
• Events (4D occurrences)
• Do not need a time-indexed parthood relation
• Happen in time
• Do not change in time (as a whole...)
• All parts are essential
• Only some proper parts are present whenever they are present (partial
presence,temporal parts)
• Objects participate to Events

PhD course on conceptual modeling and ontological analysis
Instances, classes, and particualrs
• Being instance-of something vs. being an instance
– Is “instancehood” a relative status?
– Are there “ultimate instances”?
• is the young Beethoven an instance of Beethoven?
• Instances vs. particulars
• “instance” may be a relative notion
• “particular” is not!
• concrete entities are all particulars
• so-called “temporal instances” are either parts of a particular or instances
of an abstract class
11

12
Qualities and qualia
• Linguistic evidence
• This rose is red
• Red is a color
• This rose has a color
• The color of this rose turned to brown in one week
• Red is opposite to green and close to brown
• The patient’s temperature is increasing
• The doctor measured the patient's temperature
• Each object or event comes with certain qualities that permanently inhere to it
and are unique of it
• Qualities are perceptually mapped into qualia, which are regions of quality
spaces.
• Properties hold because qualities have certain locations in their quality spaces.
• Each quality type has its own quality space

13
Qualities
The rose and the chair have the same color:
• different color qualities inhere to the two objects
• they are located in the same quality region
Therefore, the same color attribute (red) is ascribed to the two
objects

14
Qualities
Color of rose1 Red421Rose1
Inheres Has-quale
Rose Color
Color-space
Red-obj
Quality
Red-region
Has-part
Has-part
Quality attribution Quality space
q-location

15
What’s special with qualities?
• A simple attribute-value structure is not enough as a
representation formalism: you need to put individual qualities
in the domain of discourse
• Differently from instances of other ottributes, individual qualities
are existentially dependent on their bearers
• The so-called determinable/determinate issue is not actually an
issue:
• All regions in a quality space correspond to determinables
• Corresponding properties holding for objects with qualities in these
spaces are determinate
• Red-color vs. red-thing...
• redness (a quality type) is very different from red (a color region)
and has a quality space very different from that of colors...

16
Qualities vs. Features
• Features: “parasitic” physical entities.
• relevant parts of their host…
… or places
• Features have qualities, qualities have
no features.

Open issues
• Spatial and temporal location as qualities?
• Binary quality spaces?
• Multiple quality spaces allowed for a single quality kind?
• Relationships among qualities, dimension analysis
• Measurement
17

18
Abstract vs. Concrete Entities
• Concrete:
• located (at least) in time
• Abstract - two meanings:
- Result of an abstraction process (something common to multiple
exempliﬁcations)
☛ Not located in space-time (no inherent spatial or temporal
location)
• Examples: propositions, sets, symbols, regions, etc.
• Quality regions and quality spaces are abstract entities
• Mereological sums (of concrete entities) are concrete, the
corresponding sets are abstract...

19
Physical vs. Non-physical Objects
• Physical objects
• Inherent spatial localization
• Not necessarily dependent on other objects
• Non-physical objects
• No inherent spatial localization
• Dependent on agents
• mental (depending on singular agents)
• social (depending on communities of agents)
• Agentive: a company, an institution
• Non-agentive: a law, the Divine Comedy, a linguistic system…
• Descriptions, an extension of DOLCE
FIAT Co.

20
Mapping with lexicons: the OntoWordNet project
(Aldo Gangemi, Alessandro Oltramari, Massimiliano Ciaramita)
• 809 synsets from WordNet1.6 directly subsumed by a DOLCE+ class
• Whole WordNet linked to DOLCE+
• Lower WordNet levels still need revision
• Glosses being transformed into DOLCE+ axioms
• Machine learning applied jointly with foundational ontology
• WordNet “domains” being used to create a modular, general purpose domain
ontology
• Ongoing work on ontological analysis of speciﬁc WordNet domains (cognition,
emotion, psychological feature)
• Ongoing cooperation with Princeton University.

21
The OntoWordNet methodology
1. Populate a general ontology (DOLCE) by adding single synsets (or whole taxonomy
branches) from a c. lexicon (upon suitable classiﬁcation)
2. Restructure a c. lexicon by checking ontological constraints (e.g. OntoClean meta-
properties) throughout the branches
3. Merge an ontology and a c. lexicon (includes 1. and 2.)
4. Enrich the resulting structure by extracting relationships from the glosses.

23
Basic Relations
• Parthood
• Between quality regions (immediate)
• Between arbitrary objects (temporary)
• Dependence
• Speciﬁc/generic constant dependence
• Constitution
• Inherence (between a quality and its host)
• Quale
• Between a quality and its region (immediate, for unchanging entities)
• Between a quality and its region (temporary, for changing entities)
• Participation
• Representation

24
Axiomatizing basic relations
• Domain restrictions
• Ground axioms (mainly algebraic)
• Links to other relations
• Dependence on time

25
Domain restrictions on basic relations
Parthood: “x is part of y”
P(x, y) → (AB(x) ∨ PD(x)) ∧ (AB(y) ∨ PD(y))
Temporary Parthood: “x is part of y during t”
P(x, y, t) → (ED(x) ∧ ED(y) ∧ T(t))
Constitution: “x constitutes y during t”
K(x, y, t) → ((ED(x) ∨ PD(x)) ∧ (ED(y) ∨ PD(y)) ∧ T(t))
Participation: “x participates in y during t”
PC(x, y, t) → (ED(x) ∨ PD(y) ∧ T(t))
Quality: “x is a quality of y”
qt(x, y) → (Q(x) ∧ (Q(y) ∨ ED(y) ∨ PD(y)))
Quale: “x is the quale of y (during t)”
ql(x, y) → (TR(x) ∧ TQ(y))
ql(x, y, t) → ((PR(x) ∨ AR(x)) ∧ (PQ(y) ∨ AQ(y)) ∧ T(t))

26
Kinds of dependence
(D1) SD(x, y) =df ο(∃t(PR(x, t)) ∧ ∀t(PR(x, t) → PR(y, t))) (Specific Const. Dep.)
(D2) SD(φ, ψ) =df DJ(φ, ψ) ∧ ο∀x(φ(x) → ∃y(ψ(y) ∧ SD(x, y))) (Specific Const. Dep.)
(D3) GD(φ, ψ) =df DJ(φ, ψ) ∧ ο(∀x(φ(x) → ∃t(PR(x, t)) ∧
∀x,t((φ(x) ∧ At(t) ∧ PR(x, t)) → ∃y(ψ(y) ∧ PR(y, t)))) (Generic Const. Dep.)
(D4) D(φ, ψ) =df SD(φ, ψ) ∨ GD(φ, ψ)) (Constant Dependence)
(D5) OD(φ, ψ) =df D(φ, ψ) ∧ ¬D(ψ, φ) (One-sided Constant Dependence)
(D6) OSD(φ, ψ) =df SD(φ, ψ) ∧ ¬D(ψ, φ) (One-sided Specific Constant Dependence)
(D7) OGD(φ, ψ) =df GD(φ, ψ) ∧ ¬D(ψ, φ) (One-sided Generic Constant Dependence)
(D8) MSD(φ, ψ) =df SD(φ, ψ) ∧ SD(ψ, φ) (Mutual Specific Constant Dependence)
(D9) MGD(φ, ψ) =df GD(φ, ψ) ∧ GD(ψ, φ) (Mutual Generic Constant Dependence)

28
Primitive relations and basic categories

30
Participation relations
• Hold between a perdurant and its involved endurants
• Extremely relevant for domain modelling
• Current axiomatization covers:
• constant vs. temporary
• complete vs. partial
• Further distinctions are currently primitive (thematic roles)
• Agent, Theme, Substrate, Instrument, Product
• More is needed on event structure, intentionality, and artifacts to
produce analytic deﬁnitions

12
Structuring events: thematic relations
•! Agent (the active role, the one who acts in the event)
• Theme/Patient (the one who undergoes the event; the patient changes its state,
the theme does not)
• Goal (what the event is directed towards – typically a desired state of affairs)
• Recipient/Beneficiary (the one who receives the effects of the event)
• Instrument (something that is used in the performance of the event)
• Location (where the event takes place)
• Time/duration (when the event takes place, or how long it lasts)

Thematic relations in service commitment
3

Thematic relations in service process
4

5
Classes and individuals
10 Overloading ISA: instantiation (2/3)
According to this taxonomy my car is a Fiat model.
FiatModel
FiatPanda
KS
mycar
OO
77
• What Fiat models do you sell?
Answer should NOT include my car.
• How can this problem be solved?

Classes and individuals (2)
6
11 Overloading ISA: instantiation (3/3)
A possible solution: has model relation.
FiatModel
FiatPanda
KS
mycar
OO
77 FiatModel Car
EconModel
KS
fiatpanda
OO
77
mycar
OO
has modeloo
• has model(mycar, fiatpanda)
• has model is a relation between individuals.
⌅ If we introduce an ISA relation between FiatModel and Car then we
deduce that fiatpanda is a car (and not a model of cars).

Links between classes
7
12 Links between properties
• Conceptual schema hold independently from speciﬁc individuals, there-
fore has model needs to be introduced as link between properties.
FiatModel Car
has modeloo
EconModel
KS
• What is the semantic of this link?
a. has model(x, y) ! Car(x) ^ FiatModel(y)
b. Car(x) ! 8y(has model(x, y) ! FiatModel(y))
c. Car(x) ! 9y(has model(x, y) ^ FiatModel(y))
⌅ No one of these semantics assures that the model of a car is unique,
however some modeling languages allow for cardinality constraints.

ISA vs. part-of
8
15 Overloading ISA: composition
Computer
Memory
KS
DiskDrive
ck
MicroDrive
KS
Computer
Memory
✏✏
has part
DiskDrive
''
has part
MicroDrive
KS

Multiple links between classes
9
17 Multiple links between properties (2/3)
Computer
Memory
✏✏
has part
DiskDrive
&&
has part
• According to semantics (a):
has part(x, y) ! Computer(x) ^ Memory(y)
has part(x, y) ! Computer(x) ^ DiskDrive(y)
• According to semantics (b):
Computer(x) ! 8y(has part(x, y) ! Memory(y))
Computer(x) ! 8y(has part(x, y) ! DiskDrive(y))
⌅ Both semantics (a) and (b) become inconsistent by assuming that
DiskDrive and Memory are disjoint: DiskDrive(x) ! ¬Memory(x).

Multiple links between parts (2)
10
18 Multiple links between properties (3/3)
Computer
Memory
✏✏
has part
DiskDrive
''
has part
MicroDrive
KS
Computer
has part
// CompPart
Memory
19
DiskDrive
KS
MicroDrive
KS
• A possible solution in the case of disjointness requires the introduction
of a new class: the class of computer parts.
• Note that, di↵erently from semantics (c), we are not claiming that
computers need to have both a memory and a disk drive, but only
that computers need to have at least a computer part and that both

11
Conclusion
• Subtle meaning distinctions do matter
• Formal ontological analysis provides a rigorous
methodology to obtain robust and coherent theories
• A humble interdisciplinary approach is essential
…Is this hard?
Of course yes!
(Why should it be easy??)

Ph d course on formal ontology and conceptual modeling

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