INTRODUCTION TO ARTIFICIAL
INTELLIGENCE
Massimo Poesio
LECTURE 5: Ontologies and Formal
Ontologies
LOGIC vs ONTOLOGIES
• Logic is not ‘knowledge’: is just a language for
encoding knowledge and inferences
• Already Aristotle realized that we need a
separate theory of what types of objects there
are, what properties they have, and how they
are related, and made a first attempt in his
CATEGORIES
• Now this area of research is known as
(Formal) ontology
PHILOSOPHICAL BACKGROUND
• Aristotle’s Metaphysics:
– A list of 10 categories
– Criteria for definition of categories
• Tree of Porphiry: Organize categories under
SUBSTANCE in a hierarchy
• Brentano: all ten categories
• Kant: neutral as to whether these categories
really reflect the world or merely our
conception of it
ARISTOTLE’s CATEGORIES
•
•
•
•
•
•
•
•
•
•
SUBSTANCE (man, horse)
QUALITY (white, heavy)
QUANTITY (four-foot, five-foot)
ACTIVITY (cutting, burning)
NB: simultaneously a
PASSIVITY (being cut, being burned)
classification of what is
SPATIALITY / LOCATION (in the there
Lyceum)
and what
TEMPORALITY / LOCATION (yesterday,
propertieslast
thereyear)
may be
RELATION (double, half)
HAVING / STATE (has shoes on)
SITUATEDNESS / POSTURE (is lying, is sitting)
DEFINITION OF CONCEPTS
(Aristotle’s Metaphysics, Book Z)
“a definition is an account, and every account
has parts, and part of the account stands to
part of the thing in just the same way that
the whole account stands to the whole thing”
= Most concepts encode necessary and
sufficient conditions for their own application
DEFINITIONS BY GENUS AND
DIFFERENTIA
MAN = RATIONAL ANIMAL
DEFINIENDUM
DEFINIENS
Definition by genus and differentia
• The ‘method of division’:
– Begin with the broadest genus containing the
species to be defined (‘ANIMAL’)
– Divide the genus in two sub-parts by some
differentia (‘FOOTED’)
– Then divide the two sub-types again (CLOVENFOOTED)
THE TREE OF PORPHIRY
Other philosophers
The greatest part of the Ideas, that make our
complex Idea of GOLD, are YELLOWNESS, great
WEIGHT, FUSIBILITY, and SOLUBILITY IN AQUA
REGIA (Locke)
In the case of many words … it is possible to
specify their meaning by reference to other
words. E.g., “ARTHROPODES” are ANIMALS
with SEGMENTED BODIES and JOINTED LEGS.
(Carnap)
`BOTTOM-UP’ ONTOLOGIES IN AI
• The interest of Artificial Intelligence
researchers in these ideas was born out of
attempts to model knowledge in specific
domains
THE BLOCKS WORLD
A BLOCKS WORLD ONTOLOGY
OBJECT
GRASPABLE
grasp(arm,x)
NON- GRASPABLE
~grasp(arm,x)
STACKABLE
stack(x,y)
CUBE
PYRAMID
~stack(x,y)
TODAY’s DOMAIN-SPECIFIC
ONTOLOGIES
• Protein Ontology: developed to codify in a
systematic way our knowledge about proteins
– http://pir.georgetown.edu/pro/
• Other ontologies listed on OPEN BIOMEDICAL
ONTOLOGY
– http://www.obofoundry.org/
– Gene ontology, C. elegans, etc
• Medical domain: UMLS
PROTEIN ONTOLOGY
UPPER ONTOLOGIES
• The work on domain-specific ontologies
eventually led to the desire to develop ontologies
that could ‘connect’ formalizations in one domain
with formalizations in other domains
– E.g., an ontology for biology with an ontology for
medicine
– But also an ontology of art with an ontology for
tourism
• Whether this is actually possible is a deep
philosophical question
CYC
• One of the first attempts in AI to produce such
an overarching ontology was done in the CYC
project – an effort to produce an
enCYClopedia of commonsense knowledge
THE CYC ONTOLOGY
http://www.cyc.com/
PROBLEMS ENCOUNTERED IN CYC
• The researchers working on CYC found
themselves confronting every single issue in
knowledge representation
• E.g., how to define VIDEOTAPE?
– A strip of coated plastic? (concrete)
– The information contained on that strip?
(abstract)
FORMAL ONTOLOGIES
• Work on formal ontologies is concerned with
providing an inferential characterization of
categories in terms of logic
• A simple example of inference:
– if X is a PHYSICAL OBJECT, then moving X from L1 to L2
implies that the LOCATION of X after the movement is
L2
• A more complex inference:
– Moving X with mass M from L1 to L2 implies that the
total mass at L1 is reduced by M, whereas the total
mass at L2 is increased by M (this is not true if X is an
abstract object)
UPPER ONTOLOGIES: DOLCE
• Work on specifying the ‘categories of
existence’ is exemplified by DOLCE, an upper
ontology developed by the Lab for Applied
Ontology of CNR (Povo)
DOLCE’S TAXONOMY
PT
Particular
ED
Endurant
PED
Physical
Endurant
M
Amount of
Matter
F
Feature
PD
Perdurant
NPED
Non-physical
Endurant
POB
Physical
Object
…
AS
Arbitrary
Sum
NPOB
Non-physical
Object
Q
Quality
EV
Event
STV
Stative
ACH
ACC
Achievement Accomplishment
…
…
TQ
Temporal
Quality
ST
State
PRO
Process
…
…
… TL
Temporal
Location
PQ
Physical
Quality
AB
Abstract
… Fact
AQ
Abstract
Quality
… SL
Spatial
Location
…
TR
Temporal
Region
…
APO
Agentive
Physical
Object
NAPO
Non-agentive
Physical
Object
MOB
Mental Object
SOB
Social Object
ASO
Agentive
Social Object
SAG
Social Agent
NASO
Non-agentive
Social Object
SC
Society
T
Time
Interval
Set
PR
Physical
Region
… S
Space
Region
R
Region
AR
Abstract
Region
…
FUNDAMENTAL ONTOLOGICAL
CHOICES IN DOLCE
• CONCRETE: ‘rock’
– Exists in space / time
• ABSTRACT: ‘law’
– Does not exists in space time
FUNDAMENTAL ONTOLOGICAL
CHOICES IN DOLCE
• ENDURANT vs PERDURANT
– ENDURANT OBJECTS: have a stable identity over a
period of time (e.g., concrete objects)
– PERDURANT OBJECTS: events that occur and then
exist no more
FUNDAMENTAL ONTOLOGICAL
CHOICES IN DOLCE
• QUALITIES
– The particular qualities of specific objects (e.g.,
the specific color of this specific slide, the
particular weight of this particular laptop, etc)
– Each quality associated with a QUALITY SPACE that
specifies the range of values that quality may take
FORMALIZATIONS OF RELATIONS
• Arguably most of the work on formal ontology
is concerned with the formalization of
RELATIONS
– PARTS
– SPACE
– TIME
PART-OF RELATION(S)
• A great variety of relations between objects
could be called ‘part’:
– My hand is part of my body
– The handle of the door
– The top of the cupboard
– This dish is made up of pepper and cod
– This atom has one electron
A SINGLE PART-OF RELATION?
• In MEREOLOGY (Lesniewski, 1927-31; Link,
1983; Simons, 1987); a single transitive part-of
relation is proposed
• Problems: intransitivity
– Marguerite’s tail is part of Marguerite the cow
– Marguerite the cow is part of the herd
– But: Marguerite’s tail is not part of the herd
Winston et al’s classification
• Winston et al (1987) distinguish between six
types of part relation:
– COMPONENT-INTEGRAL OBJECT (handle / cup)
– PORTION-WHOLE(slice / pie)
– SUBSTANCE-WHOLE(steel / bike)
– MEMBER-COLLECTION (tree / forest)
– FEATURE-ACTIVITY (paying / shopping)
– PLACE-AREA (oasis / desert)
VIEU & ARNAGUE 2007
• Vieu & Arnague show that many of the ‘part-of’
relations can be distinguished using a limited number
of categories:
– PLURALITY
• Both ELEMENT-COLLECTION and SUB-COLLECTION –COLLECTION
require one (or two) of the relata to be collections
– SUBSTANCE
• PORTION-WHOLE and SUBSTANCE-WHOLE require one of the
relata to be a substance
• This leaves out
– ‘PART’ proper, Component-Integral Whole (CIW)
– Temporal and spatial part
COMPONENT-INTEGRAL-WHOLE
• Main claim: an account of the ‘proper’ part
relation requires an account of
FUNCTIONALITY
– Part of what makes a object a ‘hand’ or a ‘wheel’
is the function it performs
– Previous accounts: Wright, Cummins, Searle
• Wright: ‘proper function’ analyzed in terms of evolution
– Problem: doesn’t apply to non-biological entities
• Cummins: the function of a pigeon’s wing with respect
to some analytical account of the pigeon’s capacity to
fly is to generate lift and propulsion
LEXICAL TYPES
• Contrasts such as
– The motor is part of the car
– The motor is part of the vehicle
– ?? The motor is part of the ARTEFACT
• Suggest to Vieu & Arnague that CIW is a
relation between LEXICAL TYPES not
denotations
– CIW-direct(x,X,y,Y,t)
CIW: DEFINITION
PHYSICAL PART
INDIVIDUAL FUNCTIONAL DEPENDENCE
GENERIC FUNCTIONAL DEPENDENCE
CLASSIFIED AS
OTHER AREAS OF RESEARCH IN
FORMAL ONTOLOGY
• Time
• Space
• Causality
ONTOLOGIES ON THE WEB: THE
SEMANTIC WEB
• The Semantic Web (Berners-Lee et al, 2001) is
a proposal to specify the type of objects
mentioned in a Web page
AN EXAMPLE OF SEMANTICALLY MARKED PAGE
JIM HENDLER’S PAGE, SEMANTIC WEB
INFO
<BODY>
<INSTANCE KEY="http://www.cs.umd.edu/users/hendler/">
<USE-ONTOLOGY ID="cs-dept-ontology" VERSION="1.0" PREFIX="cs" URL=
"http://www.cs.umd.edu/projects/plus/SHOE/cs.html" />
<CATEGORY NAME="cs.Professor" FOR="http://www.cs.umd.edu/users/hendler/"/>
<RELATION NAME="cs.member">
<ARG POS=1 VALUE="http://www.cs.umd.edu/projects/plus/">
<ARG POS=2 VALUE="http://www.cs.umd.edu/users/hendler/">
</RELATION>
<RELATION NAME="cs.name">
<ARG POS=2 VALUE="Dr. James Hendler">
</RELATION>
<RELATION NAME="cs.doctoralDegreeFrom">
<ARG POS=1 VALUE="http://www.cs.umd.edu/users/hendler/">
<ARG POS=2 VALUE="http://www.brown.edu">
</RELATION>
<RELATION NAME="cs.emailAddress">
<ARG POS=2 VALUE="[email protected]">
</RELATION>
…..
</INSTANCE>
<b>As of January 1, 2007 Professor Hendler has moved from the University of Maryland to <a
href="http://www.rpi.edu">Rensselaer Polytechnic Institute</a></b>.
SEMANTIC WEB INGREDIENTS
• XML as a language of markup
• RDF as the basic tool for representing
information
• OWL (Web Ontology Language) to describe
concepts, attributes, and relations
• One or more ontologies
RESOURCE DESCRIPTION FRAMEWORK
(RDF)
• A language to describe statements of the
form: <RESOURCE, PROPERTY, VALUE>
‘Il presidente Ciampi vive a Roma’
RDF EXAMPLE
<?xml version='1.0'?>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:wikipedia="http://it.wikipedia.org/wiki/"
xmlns:wikidizionario="http://it.wiktionary.org/wiki/">
<rdf:Description rdf:about="http://www.quirinale.it/presidente/ciampi.htm">
<wikidizionario:vivere
rdf:resource="http://www.comune.roma.it/index.asp"/>
<wikipedia:codice_fiscale> CMPCLZ20T09E625V
</wikipedia:codice_fiscale>
</rdf:Description>
</rdf:RDF>
OWL: A LANGUAGE TO DESCRIBE
ONTOLOGIES
• A series of languages allowing increasingly
more complex descriptions
– OWL-LITE: taxonomies, restrictions
– OWL-DL: Description Logics (see next week)
– OWL-FULL: Maximum expressivity
OWL
<owl:Class rdf:ID="ProteinComplex">
<owl:disjointWith> <owl:Class rdf:ID="SiteGroup"/>
</owl:disjointWith>
<owl:disjointWith> <owl:Class rdf:about="#Chains"/>
</owl:disjointWith>
<owl:disjointWith> <owl:Class rdf:about="#Residues"/>
</owl:disjointWith>
READINGS
• Sowa, Knowledge Representation, Brooks &
Cole, chapter 2
• Vieu & Arnague (2007), Part-of Relations,
Functionality and Dependence, In Aurnague,
M.; Hickmann, M. and Vieu, L. (eds.), The
Categorization of Spatial Entities in Language
and Cognition, John Benjamins, p. 307-337.