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Title: Ontologies:%20perspectives,%20formal%20languages%20and%20tools%20%20%20Dipartimento%20di%20Informatica,%20Sistemistica%20e%20Comunicazione%20Universit


1
Ontologies perspectives, formal languages and
tools Dipartimento di Informatica,
Sistemistica e ComunicazioneUniversità di
Milano-Bicocca
  • bandini_at_disco.unimib.it tel. 02 6448 7835
  • tel. 02 6448 7879
  • ale.m_at_disco.unimib.it
  • matteo.palmonari_at_disco.unimib.it

2
What are Ontologies?
  • Philosophy
  • Where philosophical ontology has been concerned
    with the furniture and entities of reality, i.e.,
    with the study of being qua being, computer
    scientists have been occupied with the
    development of formalized, semantic, and
    logic-based models, which can easily be
    implemented in computer systems.
  • ontology may be defined as the study of being
    as such
  • Peter Øhrstrøm, Jan Andersen, Henrik Scharfe,
    What Has Happened to Ontology In F. Dau, M.-L.
    Mugnier, G. Stumme (Eds.) ICCS 2005, LNAI 3596,
    pp. 425438, 2005. Springer-Verlag Berlin
    Heidelberg 2005.
  • Ontology, understood as a branch of metaphysics,
    is the science of being in general, embracing
    such issues as the nature of existence and the
    categorical structure of reality. ... Different
    systems of ontology propose alternative
    categorical schemes. A categorical scheme
    typically exhibits a hierarchical structure, with
    'being' or 'entity' as the topmost category,
    embracing everything that exists.
  • Honderich, T. (Ed.). (1995). The Oxford companion
    to philosophy. New York Oxford University Press.

Computer Science An ontology is a specification
of a conceptualization. T. R. Gruber. A
translation approach to portable ontologies.
Knowledge Acquisition, 5(2)199-220, 1993.
3
What are Ontologies?
  • Philosophy
  • Where philosophical ontology has been concerned
    with the furniture and entities of reality, i.e.,
    with the study of being qua being, computer
    scientists have been occupied with the
    development of formalized, semantic, and
    logic-based models, which can easily be
    implemented in computer systems.
  • ontology may be defined as the study of being
    as such
  • Peter Øhrstrøm, Jan Andersen, Henrik Scharfe,
    What Has Happened to Ontology In F. Dau, M.-L.
    Mugnier, G. Stumme (Eds.) ICCS 2005, LNAI 3596,
    pp. 425438, 2005. Springer-Verlag Berlin
    Heidelberg 2005.
  • Ontology, understood as a branch of metaphysics,
    is the science of being in general, embracing
    such issues as the nature of existence and the
    categorical structure of reality. ... Different
    systems of ontology propose alternative
    categorical schemes. A categorical scheme
    typically exhibits a hierarchical structure, with
    'being' or 'entity' as the topmost category,
    embracing everything that exists.
  • Honderich, T. (Ed.). (1995). The Oxford companion
    to philosophy. New York Oxford University Press.

Computer Science An ontology is a specification
of a conceptualization. T. R. Gruber. A
translation approach to portable ontologies.
Knowledge Acquisition, 5(2)199-220, 1993.
4
What are Ontologies?
  • Philosophy
  • Where philosophical ontology has been concerned
    with the furniture and entities of reality, i.e.,
    with the study of being qua being, computer
    scientists have been occupied with the
    development of formalized, semantic, and
    logic-based models, which can easily be
    implemented in computer systems.
  • ontology may be defined as the study of being
    as such
  • Peter Øhrstrøm, Jan Andersen, Henrik Scharfe,
    What Has Happened to Ontology In F. Dau, M.-L.
    Mugnier, G. Stumme (Eds.) ICCS 2005, LNAI 3596,
    pp. 425438, 2005. Springer-Verlag Berlin
    Heidelberg 2005.
  • Ontology, understood as a branch of metaphysics,
    is the science of being in general, embracing
    such issues as the nature of existence and the
    categorical structure of reality. ... Different
    systems of ontology propose alternative
    categorical schemes. A categorical scheme
    typically exhibits a hierarchical structure, with
    'being' or 'entity' as the topmost category,
    embracing everything that exists.
  • Honderich, T. (Ed.). (1995). The Oxford companion
    to philosophy. New York Oxford University Press.

The subject of ontology is the study of the
categories of things that exist or may exist in
some domain. The product of the study, called an
ontology, is a catalog of the types of things
that are assumed to exist in a domain
of interest, D, from the perspective of a person
who uses language L for the purpose of talking
about D. Sowa, John F. Knowledge Representation.
Logical, Philosophical, and Computational
Foundations, Brooks Cole Publishing Co., Pacific
Grove, CA, (2000).
"on the other hand, in its most prevalent use
in AI, an ontology refers to an engineering
artifact, constituted by a specific vocabulary
used to describe a certain reality, plus a set of
explicit assumptions regarding the intended
meaning of the vocabulary words." Guarino, N.
Formal Ontology in Information Systems. in
Guarino, N. (ed) Proceedings of FOIS98, IOS
Press, Amsterdam Trento, Italy, pp. 315, (1998).
Computer Science An ontology is a specification
of a conceptualization. T. R. Gruber. A
translation approach to portable ontologies.
Knowledge Acquisition, 5(2)199-220, 1993.
5
Why Ontologies in CS?
  • Applications
  • E-commerce, Ubiquitous Computing, Expert Systems,
    ERP, e-Government, etc
  • System Modeling and Design
  • (AI and Expert Systems, Object Oriented
    Programming)
  • Which Entities need to be esplicitely
    represented?
  • Which Objects need to be represented?
  • Semantic Web
  • Integration and Interoperability
  • Semantic Web Services
  • Related to both Semantic Web and Interoperability
  • Information Retrieval
  • Natural Language Processing

6
Why Ontologies in CS?
  • Applications
  • E-commerce, Ubiquitous Computing, Expert Systems,
    ERP, e-Government, etc
  • System Modeling and Design
  • (AI and Expert Systems, Object Oriented
    Programming)
  • Which Entities need to be esplicitely
    represented?
  • Which Objects need to be represented?
  • Semantic Web
  • Integration and Interoperability
  • Semantic Web Services
  • Related to both Semantic Web and Interoperability
  • Information Retrieval
  • Natural Language Processing

7
Semantic Web
  • The Semantic Web aims for machine-understandable
    Web resources, whose information can then be
    shared and processed both by automated tools,
    such as search engines, and by human users.
  • Sharing of information between dierent agents
    requires semantic mark-up, i.e., an annotation of
    the Web page with information on its content that
    is understood by the agents searching the Web.
  • Such an annotation will be given in some
    standardized, expressive language (which, e.g.,
    provides Boolean operators and some form of
    quantication) and make use of certain terms (like
    Human", Plant", etc.).
  • To make sure that dierent agents have a common
    understanding of these terms, one needs
    ontologies in which these terms are described,
    and which thus establish a joint terminology
    between the agents.
  • Basically, an ontology is a collection of
    denitions of concepts and the shared
    understanding comes from the fact that all the
    agents interpret the concepts w.r.t. the same
    ontology.
  • Reasoning is important to ensure the quality of
    an ontology !

Franz Baader, Ian Horrocks, and Ulrike Sattler.
Description logics as ontology languages for the
semantic web. In Lecture Notes in Artificial
Intelligence 2605, pages 228-248. Springer, 2005.
8
Integration and Interoperability
  • Data integration (integration of different
    databases)
  • Query across different databases
  • Integration
  • Application integration (interoperability,
    information exchange and knowledge sharing)


e.g.1 - Find all horses
e.g.2 - Find all horses racing in Italy
horses (with attribute racing country)
cavalli che corrono in italia
Taken from M. Lenzerini, Information
Integration, invited tutorial to Eighteenth
International Joint Conference on Artificial
Intelligence, IJCAI 2003
9
Service Oriented Computing with Semantic Web
Services
  • Interoperability through Service Oriented
    Application
  • WS publishing, discovery, selection,composition,
    execution
  • Annotation of resources (services)
  • Semantic descriptions of the offered services
  • Semantic specification of users goal
  • Discovery of w-services basd on semantic matching
  • Semantic based mediations
  • e.g. when Looking for a WS selling a trip to
    france...
  • .... pick up a service offering a trip to Paris
  • .... pick up a service offering a trip to Paris,
    Lyon, Nice
  • .... Not pick up a service offering a trip from
    Paris to Bruxels
  • Require the specification of
  • what is a trip where is Paris, Lyon, Nice,
    Bruxels (relationship between France and cities
    within France)

10
E.G Virtual Travel Agency Service Description
  • book tickets, hotels, amenities, etc.
  • capability description (pre-state)

capability VTAcapability sharedVariables
?creditCard, ?initialBalance, ?item,
?passenger precondition definedBy
?reservationRequest reservationItem
hasValue ?item, passenger hasValue
?passenger, payment hasValue
?creditcard, memberOf trreservationReques
t and ((?item memberOf trtrip) or (?item
memberOf trticket)) and ?creditCardbalance
hasValue ?initialBalance memberOf
pocreditCard. assumption definedBy
povalidCreditCard(?creditCard) and
(?creditCardtype hasValue povisa or
?creditCardtype hasValue pomastercard).
Taken from DERI-WSMO Web Service Tutorial at
ISWC 05
11
How to represent Ontologies?
  • Need for languages... formal, machine readable,
    (standardized?) for the ontological
    representations
  • Concepts ... Conceptual entities of a domain
    (e.g. Horse)
  • Properties ... Attributes describing concepts
    (e.g. hasColor)
  • Relations ... Relations among concepts (e.g. Is-A
    Animal)
  • Axioms ... Constraints and committments on the
    ontological representation (e.g. No horse is a
    human)
  • Individuals and memberships (e.g. Furia is a
    Horse)
  • Reasoning is important to
  • Ensure the quality of an ontology during ontology
    design
  • it can be used to test whether concepts are
    non-contradictory and to derive implied
    relations.
  • test whether the concept denitions in the
    ontology have the intended consequences or not.
  • When searching Web pages, data and documents
    annotated with such concepts.
  • E.g. Want to find all resources about Funky Music
  • Pick up also those about Deep Funk, Afro-Funk,
    Afro-Soul (i.e. subconcept)
  • Pick up also those about Soul Music (i.e. similar
    concept)
  • Artificial Intelligence and KR has a long
    tradition!

12
FOL !
Termini
Formule Atomiche
Formule ben formate
GREAT EXPRESSIVITY, BUT WHAT ABOUT
REASONING? Many Calculi, but computability
problems! FOL is undecidable!
13
Semantic Nets
What about reasoning?
14
E.g. Frame
What about reasoning?
15
E.g. Logic Programming
What about reasoning?
Sfumatura di località con relazione di
contiguità (simmetrica, riflessiva). La vicinanza
non è transitiva. vicino(LUOGO, LUOGO) -
luogo(LUOGO). vicino(LUOGO_2, LUOGO_1) -
vicino(LUOGO_1, LUOGO_2), luogo(LUOGO_1),
luogo(LUOGO_2). -vicino(L1, L2) - not vicino(L1,
L2), luogo(L1), luogo(L2). La coincidenza
spaziale è una relazione di equivalenza tra
luoghi. coincide(L, L) - luogo(L). coincide(L1,
L2) - luogo(L1), luogo(L2), coincide(L2,
L1). coincide(L1, L3) - coincide(L1, L2),
coincide(L2, L3), luogo(L1), luogo(L2),
luogo(L3). -coincide(L1, L2) - not coincide(L1,
L2), luogo(L1), luogo(L2).
16
Ontologies
  • Conceptual Modeling
  • Representation Reasoning
  • Not FOL BALANCE between Expressiveness and
    Computational Acceptable Behavior
  • Semantic, machine-readable annotation of data,
    documents, resources (Semantic Web, SOC,
    Information retrieval, Ubiquitous Computing,...)

17
Ontologies as a (formal) technology
Representation, Semantics (Logic), Reasoning
Representation, annotation, information exchange
and standards
XML
RDF (Resource Description Language)
expressiveness complexity
SWRL
...
decidability
Frames frame logic
...
- expressiveness - complexity
Ontologies Editing, Reasoning, Navigation, Query
18
Ontologies as a (formal) technology
Representation, Semantics (Logic), Reasoning
Representation, annotation, information exchange
and standards
XML
RDF (Resource Description Language)
expressiveness
SWRL
...
decidability
Frames frame logic
...
complexity
Ontologies Editing, Reasoning, Navigation, Query
19
Ontologies as a (formal) technology
Representation, Semantics (Logic), Reasoning
Representation, annotation, information exchange
and standards
XML
RDF (Resource Description Language)
expressiveness
SWRL
...
decidability
Frames frame logic
...
complexity
Ontologies Editing, Reasoning, Navigation, Query
20
Ontologies as a (formal) technology
Representation, Semantics (Logic), Reasoning
Representation, annotation, information exchange
and standards
XML
RDF (Resource Description Language)
expressiveness
SWRL
...
decidability
Frames frame logic
...
complexity
Ontologies Editing, Reasoning, Navigation, Query
21
Ontologies and MetadataThe layer cake
(versione aggiornata)
  • Machine-processable Global Web Standard
  • Non ambiguous names with URI
  • Representing relational data and metadata (RDF)
  • Ontological representation language(RDF Schema e
    OWL)
  • Query (SparQL), rules, logic, proofs

Source http//www.w3.org/DesignIssues/diagrams/sw
-stack-2005.png
22
Modeling major representational focus...
  • Concepts ... Conceptual entities of a domain
    (e.g. Horse)
  • Properties ... Attributes describing concepts
    (e.g. hasColor)
  • Relations ... Relations among concepts (e.g. Is-A
    Animal)
  • Axioms ... Constraints and committments on the
    ontological representation (e.g. No horse is a
    human)
  • Individuals and memberships (e.g. Furia is a
    Horse)

Semantic Nets
Frames
Logic
23
RDF
  • Resource Description Language to associate
    metadata to resources available on the web
  • XML sysntax (restrictions from a specific DTD)
  • Statements subject predicate object
  • E.g. Document 1 is-about Horses
  • Uniform Resource Identifier (URI) to identify
    everything we want to talk about (resources)
  • Everything can be a resource
  • A piece of information
  • A document
  • A concept of a paticular ontology
  • ...
  • Subject / predicate / object are all resources.
  • E.g.
  • Still no reasoning! What is the difference
    between rdftype / rdfcreator / rdfisAbout

http//www.aaaa.it/document1.html
http//www.bbbb.it/Ontology/Horse
rdfisAbout
For the full RDF syntax see RDF/XML Syntax
Specification http//www.w3.org/TR/rdf-syntax-gra
mmar/
24
OWL OWL Web Ontology Language Guide W3C
Recommendation 10 February 2004
  • Obiettivi
  • Formalize a domain by defining classes and
    properties of those classes,
  • define individuals and assert properties about
    them, and
  • reason about these classes and individuals to
    the degree permitted by the formal semantics of
    the OWL language.

"Tell me what wines I should buy to serve with
each course of the following menu. And, by the
way, I don't like Sauternes. To support this
sort of computation, it is necessary to go beyond
keywords and specify the meaning of the resources
described on the Web. This additional layer of
interpretation captures the semantics of the
data. An OWL ontology may include descriptions
of classes, properties and their instances. Given
such an ontology, the OWL formal semantics
specifies how to derive its logical consequences,
i.e. facts not literally present in the ontology,
but entailed by the semantics.
25
The Species of OWL Three increasingly expressive
sublanguages
OWL Lite supports those users primarily needing a
classification hierarchy and simple constraint
features. For example, while OWL Lite supports
cardinality constraints, it only permits
cardinality values of 0 or 1. It should be
simpler to provide tool support for OWL Lite than
its more expressive relatives, and provide a
quick migration path for thesauri and other
taxonomies. OWL DL supports those users who
want the maximum expressiveness without losing
computational completeness (all entailments are
guaranteed to be computed) and decidability (all
computations will finish in finite time) of
reasoning systems. OWL DL includes all OWL
language constructs with restrictions such as
type separation (a class can not also be an
individual or property, a property can not also
be an individual or class). OWL DL is so named
due to its correspondence with description logics
Description Logics, a field of research that
has studied a particular decidable fragment of
first order logic. OWL DL was designed to support
the existing Description Logic business segment
and has desirable computational properties for
reasoning systems. OWL Full is meant for users
who want maximum expressiveness and the syntactic
freedom of RDF with no computational guarantees.
For example, in OWL Full a class can be treated
simultaneously as a collection of individuals and
as an individual in its own right. Another
significant difference from OWL DL is that a
owlDatatypeProperty can be marked as an
owlInverseFunctionalProperty. OWL Full allows an
ontology to augment the meaning of the
pre-defined (RDF or OWL) vocabulary. It is
unlikely that any reasoning software will be able
to support every feature of OWL Full.
The choice between OWL Lite and OWL DL depends on
the extent to which users require the more
expressive restriction constructs provided by OWL
DL. Reasoners for OWL Lite will have desirable
computational properties. Reasoners for OWL DL,
while dealing with a decidable sublanguage, will
be subject to higher worst-case complexity. The
choice between OWL DL and OWL Full mainly depends
on the extent to which users require the
meta-modelling facilities of RDF Schema (i.e.
defining classes of classes). When using OWL Full
as compared to OWL DL, reasoning support is less
predictable.
26
Simple Named Classes
The most basic concepts in a domain should
correspond to classes that are the roots of
various taxonomic trees. Every individual in the
OWL world is a member of the class owlThing.
Thus each user-defined class is implicitly a
subclass of owlThing. Domain specific root
classes are defined by simply declaring a named
class. OWL also defines the empty class,
owlNothing.
owlThing
Name Specification
ltowlClass rdfID"ConsumableThing"/gt
ltowlClass rdfIDRegion"/gt
ltowlClass rdfIDWinery"/gt
owlNothing
And while the classes exist, they may have no
members. For all we know at the moment, these
classes might as well have been called Thing1,
Thing2, and Thing3
27
Taxonomic Constructor for Classes rdfssubClassOf
The fundamental taxonomic constructor for classes
is rdfssubClassOf. It relates a more specific
class to a more general class. If X is a subclass
of Y, then every instance of X is also an
instance of Y. The rdfssubClassOf relation is
transitive (if X is a subclass of Y and Y a
subclass of Z then X is a subclass of Z
ltowlClass rdfID"PotableLiquid"gt ltrdfssubClassO
f rdfresource"ConsumableThing"/gt ... lt/owlClas
sgt
We define PotableLiquid (liquids suitable for
drinking) to be a subclass of ConsumableThing.
ConsumableThing
PotableLiquid
A class definition has two parts a name
introduction or reference and a list of
restrictions. Each of the immediate contained
expressions in the class definition further
restricts the instances of the defined class.
Instances of the class belong to the intersection
of the restrictions.
28
Reasoning about Individuals Instance-of
Relationship
A class is simply a name and collection of
properties that describe a set of individuals.
Individuals are the members of those sets.
Classes should correspond to naturally occurring
sets of things in a domain of discourse, and
individuals should correspond to actual entities
that can be grouped into these classes. An
individual is minimally introduced by declaring
it to be a member of a class.
ltRegion rdfID"CentralCoastRegion"/gt
ltowlClass rdfID"Grape"gt ... lt/owlClassgt
ltowlClass rdfID"WineGrape"gt ltrdfssubClassOf
rdfresource"Grape" /gt lt/owlClassgt
ltWineGrape rdfID"CabernetSauvignonGrape" /gt
Levels of representation In certain contexts
something that is obviously a class can itself be
considered an instance of something else. For
example, in the wine ontology we have the notion
of a Grape, which is intended to denote the set
of all grape varietals. CabernetSauvingonGrape is
an example instance of this class, as it denotes
the actual grape varietal called Cabernet
Sauvignon. However, CabernetSauvignonGrape could
itself be considered a class, the set of all
actual Cabernet Sauvignon grapes. Subclass vs.
instance It is very easy to confuse the
instance-of relationship with the subclass
relationship. For example, it may seem arbitrary
to choose to make CabernetSauvignonGrape an
individual that is an instance of Grape, as
opposed to a subclass of Grape. This is not an
arbitrary decision. The Grape class denotes the
set of all grape varietals, and therefore any
subclass of Grape should denote a subset of these
varietals. Thus, CabernetSauvignonGrape should be
considered an instance of Grape, and not a
subclass. It does not describe a subset of Grape
varietals, it is a grape varietal.
29
Object Properties
Properties let us assert general facts about the
members of classes and specific facts about
individuals. A property is a binary
relation. 1 object properties, relations
between instances of two classes (individuals to
individuals) 2 datatype properties, relations
between instances of classes (individuals to
datatypes)
ltowlObjectProperty rdfID"madeFromGrape"gt
ltrdfsdomain rdfresource"Wine"/gt
ltrdfsrange rdfresource"WineGrape"/gt
lt/owlObjectPropertygt ltowlObjectProperty
rdfID"course"gt ltrdfsdomain
rdfresource"Meal" /gt ltrdfsrange
rdfresource"MealCourse" /gt lt/owlObjectProperty
gt
Thing
madeFromGrape
WineGrape
Wine
Thing
30
Properties and Inference
The use of range and domain information in OWL is
different from type information in a programming
language. Among other things, types are used to
check consistency in a programming language. In
OWL, a range may be used to infer a type. For
example, given
ltowlThing rdfID"LindemansBin65Chardonnay"gt
ltmadeFromGrape rdfresource"ChardonnayGrape"
/gt lt/owlThinggt
Thing
ChardonnayGrape
LB65C
x
madeFromGrape
Wine
WineGrape
We can infer that LindemansBin65Chardonnay is a
wine because the domain of madeFromGrape is Wine
31
Taxonomy of Properties Property hierarchies may
be created by making one or more statements that
a property is a subproperty of one or more other
properties
ltowlClass rdfID"WineDescriptor"
/gt ltowlClass rdfID"WineColor"gt
ltrdfssubClassOf rdfresource"WineDescriptor"
/gt ... lt/owlClassgt ltowlObjectProperty
rdfID"hasWineDescriptor"gt ltrdfsdomain
rdfresource"Wine" /gt ltrdfsrange
rdfresource"WineDescriptor" /gt
lt/owlObjectPropertygt ltowlObjectProperty
rdfID"hasColor"gt ltrdfssubPropertyOf
rdfresource"hasWineDescriptor" /gt ltrdfsrange
rdfresource"WineColor" /gt ...
lt/owlObjectPropertygt
WineDescriptor properties relate wines to their
color and components of their taste, including
sweetness, body, and flavor.
hasColor is a subproperty of the
hasWineDescriptor property, with its range
further restricted to WineColor
32
Properties and Inference
Wine
WineDescription
hasWineDescription
subPropertyOf ?
hasColor
WineColor
Wine
WineDescription
hasColor
x
WineColor
hasWineDescription
Anything with a hasColor property with value x
also has a hasWineDescriptor property with value
x
33
At least, At most Restrictions OWL Lite
Cardinality is useful to state that a property on
a class has both minCardinality 0 and
maxCardinality 0 or both minCardinality 1 and
maxCardinality 1
ltowlClass rdfID"Wine"gt ltrdfssubClassOf
rdfresource"PotableLiquid"/gt
ltrdfssubClassOfgt ltowlRestrictiongt
ltowlonProperty rdfresource"madeFromGrape"/gt
ltowlminCardinality rdfdatatype"nonNegativeInt
eger"gt 1 lt/owlminCardinalitygt
lt/owlRestrictiongt lt/rdfssubClassOfgt
... lt/owlClassgt
A wine is made from at least one WineGrape
AnonymousClass
madeFromGrape 1
Wine
WineGrape
PotableLiquid
34
Properties of Individuals
ltRegion rdfID"SantaCruzMountainsRegion"gt
ltlocatedIn rdfresource"CaliforniaRegion" /gt
lt/Regiongt
ltWinery rdfID"SantaCruzMountainVineyard" /gt
ltCabernetSauvignon rdfID"SantaCruzMountainViney
ardCabernetSauvignon" gt ltlocatedIn
rdfresource"SantaCruzMountainsRegion"/gt
lthasMaker rdfresource"SantaCruzMountainVineyard
" /gt lt/CabernetSauvignongt
SantaCruzMountainsRegion
locatedIn
SantaCruzMountainVineyard CabernetSauvignon
hasMaker
SantaCruzMountainVineyard
35
Properties Characteristics
inverseOf One property may be stated to be the
inverse of another property. If the property P1
is stated to be the inverse of the property P2,
then if X is related to Y by the P2 property,
then Y is related to X by the P1 property
TransitiveProperty Properties may be stated to be
transitive. If a property is transitive, then if
the pair (x,y) is an instance of the transitive
property P, and the pair (y,z) is an instance of
P, then the pair (x,z) is also an instance of
P OWL Lite (and OWL DL) impose the side
condition that transitive properties (and their
superproperties) cannot have a maxCardinality 1
restriction. Without this side-condition, OWL
Lite and OWL DL would become undecidable
languages.
SymmetricProperty Properties may be stated to be
symmetric. If a property is symmetric, then if
the pair (x,y) is an instance of the symmetric
property P, then the pair (y,x) is also an
instance of P
FunctionalProperty P(x,y) and P(x,z) implies y
z Properties may be stated to have a unique
value. If a property is a FunctionalProperty,
then it has no more than one value for each
individual (it may have no values for an
individual). This characteristic has been
referred to as having a unique property.
FunctionalProperty is shorthand for stating that
the property's minimum cardinality is zero and
its maximum cardinality is 1.
InverseFunctionalProperty P(y,x) and P(z,x)
implies y z Properties may be stated to be
inverse functional. If a property is inverse
functional then the inverse of the property is
functional. Thus the inverse of the property has
at most one value for each individual. This
characteristic has also been referred to as an
unambiguous property
36
SymmetricProperty
ltowlObjectProperty rdfID"adjacentRegion"gt ltrdf
type rdfresource"SymmetricProperty"
/gt ltrdfsdomain rdfresource"Region" /gt
ltrdfsrange rdfresource"Region" /gt
lt/owlObjectPropertygt ltRegion
rdfID"MendocinoRegion"gt ltlocatedIn
rdfresource"CaliforniaRegion" /gt
ltadjacentRegion rdfresource"SonomaRegion" /gt
lt/Regiongt
The MendocinoRegion is adjacent to the
SonomaRegion and vice-versa. The MendocinoRegion
is located in the CaliforniaRegion but not vice
versa.
TransitiveProperty
ltowlObjectProperty rdfID"locatedIn"gt ltrdftype
rdfresource"TransitiveProperty"
/gt ltrdfsdomain rdfresource"owlThing"
/gt ltrdfsrange rdfresource"Region" /gt
lt/owlObjectPropertygt ltRegion
rdfID"SantaCruzMountainsRegion"gt ltlocatedIn
rdfresource"CaliforniaRegion" /gt lt/Regiongt
ltRegion rdfID"CaliforniaRegion"gt ltlocatedIn
rdfresource"USRegion" /gt lt/Regiongt
Because the SantaCruzMountainsRegion is locatedIn
the CaliforniaRegion, then it must also be
locatedIn the USRegion, since locatedIn is
transitive
37
Property Restrictions
allValuesFrom The restriction allValuesFrom is
stated on a property with respect to a class. It
means that this property on this particular class
has a local range restriction associated with it.
Thus if an instance of the class is related by
the property to a second individual, then the
second individual can be inferred to be an
instance of the local range restriction class
ltowlClass rdfID"Wine"gt ltrdfssubClassOf
rdfresource"PotableLiquid" /gt ...
ltrdfssubClassOfgt ltowlRestrictiongt
ltowlonProperty rdfresource"hasMaker" /gt
ltowlallValuesFrom rdfresource"Winery" /gt
lt/owlRestrictiongt lt/rdfssubClassOfgt ...
lt/owlClassgt
For all wines, if they have makers, all the
makers are wineries
someValuesFrom The restriction someValuesFrom is
stated on a property with respect to a class. A
particular class may have a restriction on a
property that at least one value for that
property is of a certain type
ltowlClass rdfID"Wine"gt ltrdfssubClassOf
rdfresource"PotableLiquid" /gt
ltrdfssubClassOfgt ltowlRestrictiongt
ltowlonProperty rdfresource"hasMaker" /gt
ltowlsomeValuesFrom rdfresource"Winery" /gt
lt/owlRestrictiongt lt/rdfssubClassOfgt ...
lt/owlClassgt
For all wines, they have at least one maker that
is a winery
38
Equality and Inequality
equivalentClass Two classes may be stated to be
equivalent. Equivalent classes have the same
instances. Equality can be used to create
synonymous classes. For example, Car can be
stated to be equivalentClass to Automobile. From
this a reasoner can deduce that any individual
that is an instance of Car is also an instance of
Automobile and vice versa.
equivalentProperty Two properties may be stated
to be equivalent. Equivalent properties relate
one individual to the same set of other
individuals. Equality may be used to create
synonymous properties. For example, hasLeader
may be stated to be the equivalentProperty to
hasHead. From this a reasoner can deduce that if
X is related to Y by the property hasLeader, X is
also related to Y by the property hasHead and
vice versa. A reasoner can also deduce that
hasLeader is a subproperty of hasHead and hasHead
is a subProperty of hasLeader.
sameAs Two individuals may be stated to be the
same. These constructs may be used to create a
number of different names that refer to the same
individual. For example, the individual Deborah
may be stated to be the same individual as
DeborahMcGuinness.
differentFrom An individual may be stated to be
different from other individuals. For example,
the individual Frank may be stated to be
different from the individuals Deborah and Jim.
Thus, if the individuals Frank and Deborah are
both values for a property that is stated to be
functional (thus the property has at most one
value), then there is a contradiction. Explicitly
stating that individuals are different can be
important in when using languages such as OWL
(and RDF) that do not assume that individuals
have one and only one name. For example, with no
additional information, a reasoner will not
deduce that Frank and Deborah refer to distinct
individuals.
AllDifferent A number of individuals may be
stated to be mutually distinct in one
AllDifferent statement. For example, Frank,
Deborah, and Jim could be stated to be mutually
distinct using the AllDifferent construct. Unlike
the differentFrom statement above, this would
also enforce that Jim and Deborah are distinct
(not just that Frank is distinct from Deborah and
Frank is distinct from Jim). The AllDifferent
construct is particularly useful when there are
sets of distinct objects and when modelers are
interested in enforcing the unique names
assumption within those sets of objects. It is
used in conjunction with distinctMembers to state
that all members of a list are distinct and
pairwise disjoint.
39
Beyond OWL Lite OWL DL OWL Full
oneOf (enumerated classes) Classes can be
described by enumeration of the individuals that
make up the class. The members of the class are
exactly the set of enumerated individuals no
more, no less. For example, the class of
daysOfTheWeek can be described by simply
enumerating the individuals Sunday, Monday,
Tuesday, Wednesday, Thursday, Friday, Saturday.
From this a reasoner can deduce the maximum
cardinality (7) of any property that has
daysOfTheWeek as its allValuesFrom restriction.
hasValue (property values) A property can be
required to have a certain individual as a value
(also sometimes referred to as property values).
For example, instances of the class of
dutchCitizens can be characterized as those
people that have theNetherlands as a value of
their nationality. (The nationality value,
theNetherlands, is an instance of the class of
Nationalities). disjointWith Classes may be
stated to be disjoint from each other. For
example, Man and Woman can be stated to be
disjoint classes. From this disjointWith
statement, a reasoner can deduce an inconsistency
when an individual is stated to be an instance of
both and similarly a reasoner can deduce that if
A is an instance of Man, then A is not an
instance of Woman. unionOf, complementOf,
intersectionOf (Boolean combinations) OWL DL and
OWL Full allow arbitrary Boolean combinations of
classes and restrictions unionOf, complementOf,
and intersectionOf. For example, using unionOf,
we can state that a class contains things that
are either USCitizens or DutchCitizens. Using
complementOf, we could state that children are
not SeniorCitizens. (i.e. the class Children is a
subclass of the complement of SeniorCitizens).
Citizenship of the European Union could be
described as the union of the citizenship of all
member states. minCardinality, maxCardinality,
cardinality (full cardinality) While in OWL Lite,
cardinalities are restricted to at least, at most
or exactly 1 or 0, full OWL allows cardinality
statements for arbitrary non-negative integers.
complex classes In many constructs, OWL Lite
restricts the syntax to single class names (e.g.
in subClassOf or equivalentClass statements). OWL
Full extends this restriction to allow
arbitrarily complex class descriptions,
consisting of enumerated classes, property
restrictions, and Boolean combinations. Also, OWL
Full allows classes to be used as instances (and
OWL DL and OWL Lite do not). For more on this
topic, see the "Design for Use" section of the
Guide document.
40
Representation, Semantics, Reasoning Description
Logics
41
Representation, Semantics, Reasoning Description
Logics
  • DL a family of logics.
  • Basically
  • Concepts Relations
  • Axioms about relations among concepts
  • Definitions, Subclasses, Constraints
  • Set theory perspective
  • Different DLs with different Expressiveness/Comple
    xity trade offs
  • Expressivity fragments of FOL
  • Reasoning Well known complexity analysis
    results some DLs provide a good balance between
    Exp/Comp

42
DL familys complexity MAP
43
Use a (Description) Logic
  • OWL DL based on Description Logic
  • In fact it is equivalent to
    DL
  • OWL DL Benefits from many years of DL research
  • Well defined semantics
  • Formal properties well understood (complexity,
    decidability)
  • Known reasoning algorithms
  • Implemented systems (highly optimised)
  • In fact there are three species of OWL (!)
  • OWL FULL is union of OWL syntax and RDF
  • OWL DL restricted OWL full to First Order
    fragment ( DAMLOIL)
  • OWL Lite is simpler subset of OWL DL (equiv to
    )

44
Class/Concept Constructors
  • C is a concept (class) P is a role (property) x
    is an individual name
  • XMLS datatypes as well as classes in 8P.C and
    9P.C
  • Restricted form of DL concrete domains

45
Semantics (cont.)
  • Interpretation function extends to concept
    (and role) expressions in the obvious way, i.e.

46
DL System Architecture
47
Ontology/Tbox Axioms
  • Obvious FO/Modal Logic equivalences
  • E.g., DL C v D FOL ?x.C(x) !D(x) ML
    C!D
  • Often distinguish two kinds of Tbox axioms
  • Definitions C v D or C D where C is a concept
    name
  • General Concept Inclusion axioms (GCIs) where C
    may be complex

48
Ontology Facts / Abox Axioms
  • Note using nominals (e.g., in SHOIN), can reduce
    Abox axioms to concept inclusion axioms
  • equivalent to
  • equivalent to

49
Knowledge Base Semantics
  • An interpretation I satisfies (models) an axiom A
    (I ² A)
  • I ² C v D iff CI µ DI I ² C D iff CI DI
  • I ² R v S iff RI µ SI I ² R S iff RI SI
  • I ² x 2 D iff xI 2 DI
  • I ² hx,yi 2 R iff (xI,yI) 2 RI
  • I ² R v R iff (RI) µ RI
  • I satisfies a Tbox T (I ² T ) iff I satisfies
    every axiom A in T
  • I satisfies an Abox A (I ² A) iff I satisfies
    every axiom A in A
  • I satisfies an KB K (I ² K) iff I satisfies both
    T and A

50
RDFS Syntax
  • ltowlClassgt
  • ltowlintersectionOf rdfparseType"
    collection"gt
  • ltowlClass rdfabout"Person"/gt
  • ltowlRestrictiongt
  • ltowlonProperty rdfresource"hasChild"/gt
  • ltowltoClassgt
  • ltowlunionOf rdfparseType" collection"gt
  • ltowlClass rdfabout"Doctor"/gt
  • ltowlRestrictiongt
  • ltowlonProperty rdfresource"hasChil
    d"/gt
  • ltowlhasClass rdfresource"Doctor"/gt
  • lt/owlRestrictiongt
  • lt/owlunionOfgt
  • lt/owltoClassgt
  • lt/owlRestrictiongt
  • lt/owlintersectionOfgt
  • lt/owlClassgt

51
Ontology Editing
  • With state of the art editors (e.g. Protegè)
  • Graphical support for design and editing (for
    TBox and ABox)
  • Editing and representation with Description Logic
    syntax and automatic generation of OWL and RDF
    code
  • Basic checks (e.g. OWL dialect)
  • Visualization Tools
  • Integration with state of the art reasoners, rule
    based systems and query systems

52
Sample Ontology Editing (Protégé)
53
Basic Inference Tasks
  • Knowledge is correct (captures intuitions)
  • Does C subsume D w.r.t. ontology O? (CI µ DI in
    every model I of O)
  • Knowledge is minimally redundant (no unintended
    synonyms)
  • Is C equivallent to D w.r.t. O? (CI DI in every
    model I of O)
  • Knowledge is meaningful (classes can have
    instances)
  • Is C is satisfiable w.r.t. O? (CI ? in some
    model I of O)
  • Querying knowledge
  • Is x an instance of C w.r.t. O? (xI 2 CI in every
    model I of O)
  • Is hx,yi an instance of R w.r.t. O? ((xI,yI) 2 RI
    in every model I of O)
  • Above problems can be solved using highly
    optimised DL reasoners

54
Basic Inference Tasks pragmatically..
  • Consistency checks (TBox/ABox)
  • Infer new relations (e.g. from transitive,
    symmetric or inverse properties)
  • Infer Hierarchies (via subsumption)
  • Infer type of individuals (based on axioms)

55
Resources
  • Slides from this talk
  • http//www.cs.man.ac.uk/horrocks/Slides/lpar04.pp
    t
  • FaCT system (open source)
  • http//www.cs.man.ac.uk/FaCT/
  • OilEd (open source)
  • http//oiled.man.ac.uk/
  • Protégé
  • http//protege.stanford.edu/plugins/owl/
  • W3C Web-Ontology (WebOnt) working group (OWL)
  • http//www.w3.org/2001/sw/WebOnt/
  • The DL Handbook, Cambridge University Press
  • http//books.cambridge.org/0521781760.htm

56
Example Ontology (Protégé)
57
Example Ontology (OilEd)
58
Example Ontology (Protégé)
59
Example Ontology (OilEd)
60
DL Reasoning Basics
  • Tableau algorithms used to test satisfiability
    (consistency)
  • Try to build a tree-like model of the input
    concept C
  • Decompose C syntactically
  • Apply tableau expansion rules
  • Infer constraints on elements of model
  • Tableau rules correspond to constructors in logic
    (u, t etc)
  • Some rules are nondeterministic (e.g., t, 6)
  • In practice, this means search
  • Stop when no more rules applicable or clash
    occurs
  • Clash is an obvious contradiction, e.g., A(x),
    A(x)
  • Cycle check (blocking) may be needed for
    termination
  • C satisfiable iff rules can be applied such that
    a fully expanded clash free tree is constructed
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