1. Introduction to Description Logics
Charlie Abela
Department of Artificial Intelligence

2. Introduction to Description Logics ©
Last Lectures
Introduced RDF and RDF Schema languages
Problems?
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Lecture Outline
Knowledge Representation
Description Logics: an Overview
Reasoning in DL
Different Reasoners
Suggested Reading list
The Semantic Web was not coined in a vacuum. It has its roots in a number of well consolidated areas. Research about how to represent information that can be somehow machine processable has been tackled in the area of knowledge representation. Semantic networks and frames were predecessors of the languages that we are using in the Semantic Web today. We’ll start by taking a look that what knowledge representation is and how it is used in the Semantic Web. In particular we will look at Description logics, which is the underlying logic of a number of Semantic Web languages. I will give a very brief overview of reasoning that is possible with DLs and mention the most popular reasoners in use.
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4. Knowledge Representation
Definitions:
It is a part of AI that is concerned with how an agent uses what it knows in deciding what to do [Nardi, Brachman]
The study of how to put knowledge into a form that a computer can reason with [Russell, Norvig]
It is the study of how knowledge about the world can be represented and what kinds of reasoning can be done with that knowledge [Anonymous]
Its all about encoding knowledge in such a way that computers/agents can use and reason with.
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5. Knowledge Representation Hypothesis
Any mechanically embodied intelligent process will be comprised of structural ingredients that a) we as external observers naturally take to represent a propositional account of the knowledge that the overall process exhibits, and b) independent of such external semantical attribution, play a formal but causal and essential role in engendering the behaviour that manifests that knowledge [Smith, 1982].
A successful representation of some knowledge must:
be in a form that is understandable by humans
must cause the system using the knowledge to behave as if it knows it.
To enforce these definitions, Smith states that an intelligent process must use knowledge representation whose form is understandable by humans and which causes the process to behave as if it knows what this knowledge means.
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6. Knowledge Based Systems
printColor(snow):- !, write(“It’s white”).
printColor(grass):- !, write(“It’s green”).
printColor(sky):- !, write(“It’s yellow”).
printColor(X):- write(”Beats me”).
printColor(X):- color(X,Y), !, write(!It’s ”),write(Y), write(“.”).
printColor(X):- write(“Beats me”).
color(snow,white).
color(sky,yellow).
color(X,Y):- madeOf(X,Z), color(Z,Y).
madeOf(grass,vegitation).
color(vegetation,green).
[from Brachman and Lavesque]
Which knowledge base “knows” that for e.g. snow is white or that sky is yellow?
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7. Knowledge Based-Systems II
2nd program seems to have some desirable features:
It is possible to add new tasks and easily make them depend on previous knowledge: e.g. adding a task to enumerate the objects of a given colour: coloredObjects(X,color(X,Y),Out).
It is possible to extend the existing behaviour by adding more beliefs: e.g. adding canaries are yellow: color(canaries, yellow)
debug faulty behaviour by locating erroneous beliefs of the system: e.g. change clause for the colour of the sky: color(sky, blue)
concisely explain and justify the behaviour of the system: e.g. why did the system say that grass is green?
grass is a form of vegetation: madeOf(grass,vegitation).
vegetation is green: color(vegetation,green).
A KB system should therefore, by design, have the ability to be told facts about the world and to adjust its behaviour accordingly
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8. Knowledge-Based Systems III
Within a KB it is possible to differentiate between
Intensional knowledge: general knowledge about the problem domain
color(X,Y) or printColor(X)
Extensional knowledge: knowledge which is specific to a particular scenario
color(snow,white) or madeOf(grass, vegetation)
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9. Overview of Description Logics
Description Logics (DLs) is the name given to a set of knowledge representation formalisms
DLs represent knowledge of an application domain or world
Define the relevant concepts of the domain
Use these concepts to specify properties of objects and individuals occurring in the domain
One main characteristic of DLs is their capability to provide reasoning
Infer implicit knowledge from that explicitly defined in the knowledge base.
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Logical Structures
Atomic Concepts (or Concepts):
unary predicate symbols
Atomic Roles:
binary predicates, express
relationship between concepts
Operators (constructors):
Individuals
Instances of classes
2. characterizes the concept Parent as the set of individuals having at least one filler of the role hasChild belonging to the concept Person, moreover every filler of the role hasChild must be a person.
3. Union, intersection and complement operators are interpreted as set operations to describe: a Person that is not a Female or An individual that is either a Woman or a Male
4. The number restriction denotes the individuals having at least three children and at most two female relatives.
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11. Knowledge Representation in DL
Intensional knowledge
General knowledge about problem domain.
A woman is a person and a female.
TBox contains intensional knowledge in form of terminology. It is a concept definition:
Extensional knowledge
Specific knowledge related to a particular problem.
Yanika is a female.
ABox contains assertions about individuals, called membership assertion:
A Knowledge Base (KB) is just a TBox and ABox
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Architecture of a DL KB
TBox
Description
Language
Reasoning
ABox
Knowledge Base
Application
Programs
Rules
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Reasoning
The basic inference on concept expressions in Description Logics is subsumption, typically written as
Determining subsumption is the problem of checking whether the concept denoted by C (the subsumee) is a subconcept of D (the subsumer)
If x is an instance of a class C, and C is a subclass of D, then we can infer that x is an instance of D
Another typical inference on concept expressions is concept satisfiability (consistency)
problem of checking whether a concept expression does not necessarily denote the empty concept.
A special case of subsumption: in which the subsumer is the empty concept, meaning that a concept is not satisfiable.
X instance of classes A and B, but A and B are disjoint
This is an indication of an error in the ontology
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Uses for Reasoning
Reasoning support is important for
checking the consistency of the knowledge base and the knowledge itself
checking for unintended relationships between classes
automatically classifying instances in classes
Checks like the preceding ones are valuable for
designing large ontologies, where multiple authors are involved
integrating and sharing ontologies from various sources
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15. DL Reasoning Algorithms
Earliest algorithms targeted subsumption and where called structural comparisons
Transform two input concepts into labelled graphs and test whether one could be embedded into the other
The embedded graph corresponds to the more general concept (ie the subsumer)
Tableau algorithms are focused on satisfiability
other reasoning problems like subsumption, can be solved by first reducing them to satisfiability
Concepts are negated and iterative checks for clashes (contradictions) are performed
If no clashes are found then concept is satisfiable else it is unsatisfiable
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Different Reasoners
FaCT++: a hybrid reasoner, is an optimised version of the original FaCT (Horrocks 1998)
Has a very efficient and optimized T-Box reasoning engine
distributed under a GPL license
Racer: state-of-the art TBox DL reasoner
however it is only free for universities and research labs
source code not publicly available
Pellet
based on the tableau algorithms developed for expressive DLs
Features:
Ontology analysis and repair
Entailment: entailment is the key inference
Queries are based on Jena’s RDQL
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Suggested Reading
D. Nardi, R. J. Brachman. An Introduction to Description Logics, Cambridge University Press, 2002,
(pgs 1-30)
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Next Lecture
Ontologies
Basic components
Ontology engineering
Examples
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