ph d course on formal ontology and conceptual modeling

Formal Ontology and Conceptual Modeling

Nicola GuarinoNational 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)

Focusing on content

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

syntheticlogical

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 itsown 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


2. Meanings and signs

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


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

ba {<a,b >}

ab {<b,a >}

ab {}

32

Representing Concepts as intensional relations

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

r n ∈ 2Dn

ρn : W → 2Dn(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 affairsState 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

melasame conceptualization

LI

LE

What is an ontology

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


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

syntheticlogical

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

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


Actor(Observer)

Conception


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

{b}{a}

{a,b}

{}

baa b

a ba b


Example 2: the concept of on

ba {<a,b >}

ab {<b,a >}

ab {}

32

Representing Concepts as intensional relations

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

r n ∈ 2Dn

ρn : W → 2Dn(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

3. Concepts and Conceptualizations

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:• Perception (as resulting from evolution)• Cognition and cultural experience (driven by actual needs)• (Language)





31PhD course on foundations of conceptual modelling and ontological analysis, Trento, October 2010



situations: D, ℜ)





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)



• 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


apple


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, 11-12/8/20023

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) artifactsexpressing the intended meaning of a vocabulary

in terms of primitive categories and relations describingthe 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 naturemakes them almost useless.



• 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


apple


LI

LE



• 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)








situations: D, ℜ)






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


affairsPresentationpatterns

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 theoryGlossary

Thesaurus

Taxonomy

DB/OO scheme

tennisfootballgamefield gamecourt gameathletic gameoutdoor game

game athletic game court game tennis outdoor game field game football

gameNT 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

interpretationsA - 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: onOnly 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

acb

aIndistinguishable conceptualizations

ac

ac

ac

ac

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

The problem of primitives

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


situations: D, ℜ)


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

The Ontological Level

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 makingintended 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!

Essence and Unity

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 rockDO 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 conditionsare 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 levelssimplify taxonomies

social-event

mental-event

physical-event

communication-event

perceptual-event

social-event

mental-event

physical-event

communication-event

perceptual-event

A taxonomy cleaning example

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 objectGroup of people

Country

FoodAnimal Legal agent

Amount of matterGroup

Living being

LocationAgentRed

Red apple Person

Vertebrate

Apple

CaterpillarButterfly

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



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze taxonomic links

• ~U can’t subsume +U• Living being can change parts and

remain the same, but amounts of matter can not (incompatible ICs)

• Living being is constituted of matter

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




• ~U can’t subsume +U• Physical objects can change parts and

remain the same, but amounts of matter can not (incompatible ICs)

• Physical object is constituted of matter

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




• Meta-properties fine• Identity-check fails: being alive is a

contingent property for physical objects, and an essential property for animals

• Constitution again

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




• Meta-properties fine• Identity-check fails: when an entity

stops being an animal, it does not stop being a physical object (when an animal dies, its body remains)

• Constitution again

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




• ~U can’t subsume +U• A group can’t change parts - it becomes a

different group• A social entity can change parts - it’s more

than just a group (incompatible IC)• Constitution again

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze non-rigid properties

Agent-I-U+D~R

• ~R can’t subsume +R• Subsumption is not disjunction!

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




Agent-I-U+D~R

• ~R can’t subsume +R• Another disjunction: all legal agents are persons or

organizations

Legal agent+L-U+D~R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




Caterpillar+L+U-D~R

Butterfly+L+U-D~R

Agent-I-U+D~R

Legal agent+L-U+D~R

• ~R can’t subsume +R• Apple is not necessarily food. A poison-apple,

e.g., is still an apple.• ~U can’t subsume +U• Caterpillars are wholes, food is stuff.Food

+I-O~U+D~R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




Country+L+U-D~R Caterpillar

+L+U-D~RButterfly+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



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R




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



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Look for missing types

Geographical Region


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



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Look for missing types

Geographical Region


Butterfly+L+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



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Analyze Attributions

Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

Legal agent+L-U+D~R

• No violations• Attributions are discouraged, can be confusing.• Often better to use attribute values (i.e. Apple

Color red)

Food+I-O~U+D~R

Red-I-U-D-R

Red apple+I-O+U-D~R

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Geographical Region


Butterfly+L+U-D~R


Agent-I-U+D~R

Legal agent+L-U+D~R

Food+I-O~U+D~R

Red-I-U-D-R

Red apple+I-O+U-D~R

Country+O+U-D+R

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Apple+O+U-D+R

Fruit+O+U-D+R



Geographical Region

+O-U-D+R


The backbone taxonomy

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Agent-I-U+D~R

Apple+O+U-D+R

Fruit+O+U-D+R

Food+I-O~U+D~R

Legal agent+L-U+D~R


Red apple+I-O+U-D~R

Red-I-U-D-R


Caterpillar+L+U-D~R

Butterfly+L+U-D~R

Country+O+U-D+R

Geographical Region

+O-U-D+R


Entity

Fruit

Physical object Group of people

Country

FoodAnimal Legal agent

Amount of matterGroup

Living being

LocationAgentRed

Red apple Person

VertebrateApple

CaterpillarButterfly

Organization

Social entity

Before

Entity-I-U-D+R



+O~U-D+R


Location+O-U-D+R


Person+O+U-D+R

Animal+O+U-D+R


Agent-I-U+D~R

Apple+O+U-D+R

Fruit+O+U-D+R

Food+I-O~U+D~R

Legal agent+L-U+D~R


Red apple+I-O+U-D~R


Caterpillar+L+U-D~R

Butterfly+L+U-D~R

Country+O+U-D+R

Geographical Region

+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 representationRoles 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 roleAnti-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 representationRoles 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 itsontological distinctions

2

DOLCEa 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

QQuality

PQPhysicalQuality

AQAbstractQuality

TQTemporalQuality

PDPerdurant

EVEvent

STVStative

ACHAchievement

ACCAccomplishment

STState

PROProcess

PTParticular

RRegion

PRPhysicalRegion

ARAbstractRegion

TRTemporalRegion

TTime

Interval

SSpaceRegion

ABAbstract

SetFact…

… … …

TLTemporalLocation

SLSpatial

Location

… … …

ASOAgentive

Social Object

NASONon-agentive Social Object

SCSociety

MOBMental Object

SOBSocial Object

FFeature

POBPhysicalObject

NPOBNon-physical

Object

PEDPhysicalEndurant

NPEDNon-physical

Endurant

EDEndurant

SAGSocial Agent

APOAgentive Physical Object

NAPONon-agentive

Physical Object

…

ASArbitrary

Sum

MAmount 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 Red421Rose1Inheres 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.

Formalizing DOLCE

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)

27

Quality relations

28

Primitive relations and basic categories

29

Dependence relations

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

Common Modeling Issues

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 individuals10 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 wededuce 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 Carhas 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 (2/2)

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 thatDiskDrive 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

Computerhas part // CompPart

Memory

19

DiskDrive

KS

MicroDrive

KS

• A possible solution in the case of disjointness requires the introductionof a new class: the class of computer parts.

• Note that, di↵erently from semantics (c), we are not claiming thatcomputers need to have both a memory and a disk drive, but onlythat computers need to have at least a computer part and that bothmemories and disk drives are computer parts.

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

Education

focus of ontological

upper ontology

study of content

philosophical ontology

content indexes

knowledge representation

content sign kinds

applied ontology loa