A Discussion of Some Intuitions of Defeasible Reasoning
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Lecture 8
OWL (continued)
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Four Highlights making OWL a powerful language on the top of RDFS:
The W3C Web Ontology Language (OWL) is a Semantic Web language designed to represent rich and complex knowledge about things, groups of things, and relations between things.
OWL is a computational logic-based language such that knowledge expressed in OWL can be exploited by computer programs, e.g., to verify the consistency of that knowledge or to make implicit knowledge explicit.
OWL documents, known as ontologies, can be published in the World Wide Web and may refer to or be referred from other OWL ontologies.
OWL is part of the W3C’s Semantic Web technology stack, which includes RDF, RDFS, SPARQL, etc.
Source https://www.w3.org/OWL/
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Four Highlights of OWL:
The current version of OWL, also referred to as “OWL 2”, was developed by the [W3C OWL Working Group] (now closed) and published in 2009, with a Second Edition published in 2012.
OWL 2 is an extension and revision of the 2004 version of OWL developed by the [W3C Web Ontology Working Group] (now closed) and published in 2004.
The deliverables that make up the OWL 2 specification include a Document Overview, which serves as an introduction to OWL 2, describes the relationship between OWL 1 and OWL 2, and provides an entry point to the remaining deliverables via a Documentation Roadmap.
Source https://www.w3.org/OWL/
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Enumerations with owl:oneOf
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Lecture Outline
Basic Ideas of OWL
The OWL Language
Examples
The OWL Namespace
Future Extensions
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Non-Unique-Names
OWL does not adopt the unique-names assumption of database systems
If two instances have a different name or ID does not imply that they are different individuals
Suppose we state that each course is taught by at most one staff member, and that a given course is taught by two staff members
An OWL reasoner does not flag an error
Instead it infers that the two resources are equal
Unique-name assumption
In general, when two individuals are known by different names, sometimes it is assumed they are different individuals.
This is an assumption that sometimes works (ex. Product codes) and sometimes doesn’t (ex. Social environment)
OWL does not make the unique-name assumption.
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Distinct Objects
To ensure that different individuals are indeed recognized as such, we must explicitly assert their inequality:
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Distinct Objects (2)
OWL provides a shorthand notation to assert the pairwise inequality of all individuals in a given list
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Data Types in OWL
XML Schema provides a mechanism to construct user-defined data types
E.g., the data type of adultAge includes all integers greater than 18
Such derived data types cannot be used in OWL
The OWL reference document lists all the XML Schema data types that can be used
These include the most frequently used types such as string, integer, Boolean, time, and date.
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Restriction of Features in OWL
Property Separation
The set of object properties and data type properties are disjoint
Therefore the following can never be specified for data type properties:
owl:inverseOf
owl:FunctionalProperty
owl:InverseFunctionalProperty
owl:SymmetricProperty
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Inheritance in Class Hierarchies
Range restriction: Courses must be taught by academic staff members only
Michael Maher is a professor
He inherits the ability to teach from the class of academic staff members
This is done in RDF Schema by fixing the semantics of “is a subclass of”
It is not the responsibility of an application (RDF processing software) to interpret “is a subclass of
OWL is based on Description Logic
Description Logic is a fragment of first-order logic
OWL inherits from Description Logic two assumptions:
The open-world assumption
The non-unique-name assumption
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Open-world assumption (OWA)
We cannot conclude some statement x to be false simply because we cannot show x to be true
We may not deduce falsity from the absence of truth
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Open-world assumption example
Question: “Did it rain in Tokyo yesterday?”
Answer: “I don’t know that it rained , but that’s not enough reason to conclude that it didn’t rain”
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Closed-world assumption (CWA)
Closed-world assumption allow deriving falsity from the inability to derive truth
Example:
Question: ” Was there a big earthquake disaster in Tokyo yesterday? ”
Answer: ” I don’t know that there was, but if there had been such a disaster, I’d have heard about it. Therefore I conclude that there wasn’t such a disaster”
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OWL vs Databases
Systems such as databases have tended to support closed worlds and unique names
Whereas
Knowledge representation systems and theorem plovers support open worlds and non-unique names
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QUESTION
By the use of two examples, one in databases and the other in web, describe how a database uses closed world and web uses open world assumptions.
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ANSWER
Web present data about uncounted concepts, Consider the following statement: “Tim Smith with the ID of 785654549 is a citizen of France.” Now, what if you ask “Is Tim Smith with the ID of 785654549 a citizen of Malaysia?” Under a closed world assumption, the answer is “no” whereas under the open world assumption the answer is “not known”. Web is full of such kinds of data. Hence, open world assumption is used in a system with incomplete information, to which Web belongs.
On the other hand databases usually presents data about limited concepts, say a university. For instance, if the database of UOW shows that Tim Smith with the ID of 785654549 is not UOW’s student, definitely he is not UOW’s student.
Moreover in web non-unique names are used, and two different ID may show the same resource, whereas in database this not the case
closed world assumption is applied to systems with complete information.
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Relation of OWL Description Logic Program (DLP) to other languages
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Lecture Outline
Basic Ideas of OWL
The OWL Language
Examples
The OWL Namespace
Future Extensions
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An African Wildlife Ontology –
Class Hierarchy
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An African Wildlife Ontology –
Properties
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An African Wildlife Ontology –
Plants and Trees
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An African Wildlife Ontology –
Branches
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An African Wildlife Ontology –
Leaves
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An African Wildlife Ontology –
Carnivores
that eat animals.
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An African Wildlife Ontology –
Giraffes
eat only leaves.
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An African Wildlife Ontology –
Lions
only herbivores.
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A Printer Ontology – Class Hierarchy
xdfdf
Product
padid
printer
hp-product
Laser Jet Printer
hp-printer
personal-printer
hpLaserJetPrinter
1100series
1100se
1100xi
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OWL for the Printer Ontology
form a subclass of products.
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The Printer Ontology – HP Products
Hewlett Packard
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The Printer Ontology –
Personal Printers
devices.
a subclass of printers.
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The Printer Ontology –
HP LaserJet 1100se Printers
and cost $450.
450
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The Printer Ontology – Properties
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Lecture Outline
Basic Ideas of OWL
The OWL Language
Examples
The OWL Namespace
Future Extensions
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OWL in OWL
We present a part of the definition of OWL in terms of itself
The following captures some of OWL’s meaning in OWL
It does not capture the entire semantics
A separate semantic specification is necessary
The URI of the OWL definition is defined as the default namespace
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Classes of Classes (Metaclasses)
The class of all OWL classes is itself a subclass of the class of all RDF Schema classes:
note that this definition has been stated in OWL document:
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Classes of Classes (Metaclasses) – Thing and Nothing (2)
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Class Disjointness
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Equality and Inequality
Equality and inequality can be stated between arbitrary things
In OWL Full this statement can also be applied to classes
Properties sameIndividualAs, sameAs and differentFrom
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Equality and Inequality (2)
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Properties (3)
owl:inverseOf relates two object properties:
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Lecture Outline
Basic Ideas of OWL
The OWL Language
Examples
The OWL Namespace
Future Extensions
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Future Extensions of OWL is involved with working on:
Modules and Imports
Defaults
Closed World Assumption
Unique Names Assumption
Procedural Attachments
Rules for Property Chaining
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Modules and Imports
The importing facility of OWL is very trivial:
It only allows importing of an entire ontology, not parts of it
Modules in programming languages based on information hiding: state functionality, hide implementation details
An open question is that how to define appropriate module mechanism for Web ontology languages
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Defaults
Many practical knowledge representation systems allow inherited values to be overridden by more specific classes in the hierarchy
treat inherited values as defaults
No consensus has been reached on the right formalization for the nonmonotonic behaviour of default values
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Closed World Assumption
OWL currently adopts the open-world assumption: we cannot conclude some statement x to be false simply because we cannot show x to be true
Closed-world assumption: a statement is true when its negation cannot be proved
tied to the notion of defaults, leads to nonmonotonic behaviour
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Summary
OWL is the proposed standard for Web ontologies
OWL builds upon RDF and RDF Schema:
(XML-based) RDF syntax is used
Instances are defined using RDF descriptions
Most RDFS modeling primitives are used
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