CSCE 771
Natural Language Processing
Lecture 17
Description Logics
Topics
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Chunking
Overview of Meaning
Readings:
 Text 13.5
 NLTK book 7.2
March 20, 2013
Overview
Last Time (Programming)
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Probabilistic parsing
Features and Unification
Complexity of Language
Meaning representations
Projects???
Today
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Chunking
Meaning representations
Description Logics
Projects???
Readings:
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Chapter 17.1
771 Website: Resources
Next Time: Semantics
–2–
CSCE 771 Spring 2013
Projects / presentations
–3–
CSCE 771 Spring 2013
Meaning Examples
Speech and Language Processing, Second Edition
Daniel Jurafsky and James H. Martin
–4–
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
CSCE 771 Spring 2013
First Order Predicate Logic
Speech and Language Processing, Second Edition
Daniel Jurafsky and James H. Martin
–5–
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
CSCE 771 Spring 2013
Figure 17.1
Speech and Language Processing, Second Edition
Daniel Jurafsky and James H. Martin
–6–
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
CSCE 771 Spring 2013
Variables and Quantification
–7–
http://en.wikipedia.org/wiki/First-order_logic
CSCE 771 Spring 2013
Lambda Notation
–8–
CSCE 771 Spring 2013
Semantics of First Order Logic
• Constant symbols
•
domain D
• Predicate symbols
• Function symbols
• Terms
•
•
variable is a term
a function applied to terms is a term (no predicates)
• Formulas well-formed formulas
•
predicates, equality, negations, AND, OR, , quantifiers
• Free and bound variables
• Interpretation: mapping symbols to real world
–9–
CSCE 771 Spring 2013
Forward Chaining -Backward Chaining
– 10 –
CSCE 771 Spring 2013
Resolution
C1: A OR B
C2: C OR not B
 A or C
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CSCE 771 Spring 2013
Temporal Logic – Representing time
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http://en.wikipedia.org/wiki/Temporal_logic
CSCE 771 Spring 2013
Representing Time/Tense fig 17.5
Reichenbaschs’ approach
•
E – denotes time of the event
•
R denotes reference time
•
U denotes utterance time
Speech and Language Processing, Second Edition
Daniel Jurafsky and James H. Martin
– 13 –
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
CSCE 771 Spring 2013
Semantic Networks
•
Collins and Quillian
•
Conceptual Graphs –
Sowa
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http://en.wikipedia.org/wiki/Semantic_network
CSCE 771 Spring 2013
Conceptual Graphs
http://www.jfsowa.com/
– 15 –
http://www.jfsowa.com/
CSCE 771 Spring 2013
KL-ONE
KL-ONE - a frame based knowledge representation
system
Frame-based = slot and filler
“The system is an attempt to overcome semantic
indistinctness in semantic network representations
and to explicitly represent conceptual information as
a structured inheritance network.”
– 16 –
http://en.wikipedia.org/wiki/KL-ONE
CSCE 771 Spring 2013
DAML + OIL
DAML - The DARPA Agent Markup Language
DAML+OIL is a successor language to DAML and OIL
that combines features of both.
In turn, it was superseded by Web Ontology Language
(OWL).
OIL stands for Ontology Inference Layer or Ontology
Interchange Language.
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http://www.daml.org/
http://en.wikipedia.org/wiki/DAML%2BOIL
CSCE 771 Spring 2013
Description Logic
– 18 –
CSCE 771 Spring 2013
Ontology fragment
.
– 19 –
CSCE 771 Spring 2013
Ontology refinement
.
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CSCE 771 Spring 2013
Ontological reasoning
Reasoning over ontologies
Challenges for ontology Languages
• Expressivity
• Computational Complexity
– 21 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
What Are Description Logics?
A family of logic based Knowledge Representation formalisms


Descendants of semantic networks and KL-ONE
Describe domain in terms of concepts (classes), roles
(properties, relationships) and individuals
Distinguished by:

Formal semantics (typically model theoretic)
 Decidable fragments of FOL (often contained in C2)
 Closely related to Propositional Modal & Dynamic Logics
 Closely related to Guarded Fragment

Provision of inference services
 Decision procedures for key problems (satisfiability,
subsumption, etc)
 Implemented systems (highly optimised)
– 22 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
What Are Description Logics?
A family of logic based Knowledge Representation formalisms


Descendants of semantic networks and KL-ONE
Describe domain in terms of concepts (classes), roles
(properties, relationships) and individuals
Distinguished by:

Formal semantics (typically model theoretic)
 Decidable fragments of FOL (often contained in C2)
 Closely related to Propositional Modal & Dynamic Logics
 Closely related to Guarded Fragment

Provision of inference services
 Decision procedures for key problems (satisfiability,
subsumption, etc)
 Implemented systems (highly optimised)
– 23 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
What Are Description Logics?
A family of logic based Knowledge Representation formalisms


Descendants of semantic networks and KL-ONE
Describe domain in terms of concepts (classes), roles
(properties, relationships) and individuals
Distinguished by:

Formal semantics (typically model theoretic)
 Decidable fragments of FOL (often contained in C2)
 Closely related to Propositional Modal & Dynamic Logics
 Closely related to Guarded Fragment

Provision of inference services
 Decision procedures for key problems (satisfiability,
subsumption, etc)
 Implemented systems (highly optimised)
– 24 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
DL Basics
Concept names are equivalent to unary predicates

In general, concepts equiv to formulae with one free
variable
Role names are equivalent to binary predicates

In general, roles equiv to formulae with two free variables
Individual names are equivalent to constants
Operators restricted so that:


Language is decidable and, if possible, of low complexity
No need for explicit use of variables
 Restricted form of 9 and 8 (direct correspondence with ◊ and
[])
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– 25 –
Features such as counting can be succinctly expressed
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Tbox (schema)
Man ´ Human u Male
Happy-Father ´ Man u 9 has-child
Female u …
Abox (data)
John : Happy-Father
hJohn, Maryi : has-child
Interface
Knowledge
Base
Inference System
DL System Architecture
John: 6 1 has-child
– 26 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
The DL Family
Given DL defined by set of concept and role forming operators
Smallest propositionally closed DL is ALC (equiv modal K(m))

Concepts constructed using u, t, :, 9 and 8
S often used for ALC with transitive roles (R+)
Additional letters indicate other extension, e.g.:

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H for role inclusion axioms (role hierarchy)
O for nominals (singleton classes, written {x})
I for inverse roles
N for number restrictions (of form 6nR, >nR)
Q for qualified number restrictions (of form 6nR.C, >nR.C)
E.g., ALC + R+ + role hierarchy + inverse roles + QNR = SHIQ
Have been extended in many directions
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– 27 –
Concrete domains, fixpoints, epistemic, n-ary, fuzzy, …
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
DL Semantics
Semantics defined by interpretations
An interpretation I = (DI, ¢I), where
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DI is the domain (a non-empty set)
¢I is an interpretation function that maps:
 Concept (class) name A ! subset AI of DI
 Role (property) name R ! binary relation RI over DI
 Individual name i ! iI element of DI
– 28 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
DL Semantics (cont.)
Interpretation function ¢I extends to concept (and role)
expressions in the obvious way, e.g.:
– 29 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
DL Knowledge Base
A DL Knowledge base K is a pair hT ,Ai where
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T is a set of “terminological” axioms (the Tbox)
A is a set of “assertional” axioms (the Abox)
Tbox axioms are of the form:
C v D, C ´ D, R v S, R ´ S and R+ v R
where C, D concepts, R, S roles, and R+ set of transitive
roles
Abox axioms are of the form:
x:D, hx,yi:R
where x,y are individual names, D a concept and R a role
– 30 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Knowledge Base Semantics
An interpretation I satisfies (models) a Tbox 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 R+ v R iff (RI)+ µ RI
I satisfies a Tbox T (I ² T ) iff I satisfies every axiom A in T
An interpretation I satisfies (models) an Abox axiom A (I ² A):
I ² x:D iff xI 2 DI
I ² hx,yi:R iff (xI,yI) 2 RI
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
– 31 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Short History of Description Logics
Phase 1:
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Incomplete systems (Back, Classic, Loom, . . . )
Based on structural algorithms
Phase 2:
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Development of tableau algorithms and complexity results
Tableau-based systems for Pspace logics (e.g., Kris, Crack)
Investigation of optimisation techniques
Phase 3:
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– 32 –
Tableau algorithms for very expressive DLs
Highly optimised tableau systems for ExpTime logics (e.g., FaCT,
DLP, Racer)
Relationship to modal logic and decidable fragments of FOL
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Recent Developments
Phase 4:

Mainstream applications and tools
 Databases
» Consistency of conceptual schemata (EER, UML etc.)
» Schema integration
» Query subsumption (w.r.t. a conceptual schema)
 Ontologies, e-Science and Semantic Web/Grid
» Ontology engineering (schema design, maintenance, integration)
» Reasoning with ontology-based annotations (data)

Mature implementations
 Research implementations
» FaCT, FaCT++, Racer, Pellet, …
 Commercial implementations
» Cerebra system from Network Inference (and now Racer)
– 33 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Ontology: Origins and History
a philosophical discipline—a branch of philosophy that
deals with the nature and the organisation of reality
Science of Being (Aristotle, Metaphysics, IV, 1)
Tries to answer the questions:

What characterizes being?

Eventually, what is being?
How should things be classified?
– 34 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Classification: An Old Problem
Extract from Bills of Mortality, published weekly from 1664-1830s
The Diseases and Casualties this Week:
Aged
54
Apoplectic
1
….
Suddenly
1
Surfeit
87
113
Fall down stairs
1
Teeth
Gangrene
1
…
Grief
1
Ulcer
2
Vomiting
7
Winde
8
Griping in the Guts
74
…
Plague
– 35 –
…
3880
Worms
18
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Ontology in Computer Science
An ontology is an engineering artefact consisting of:
 A vocabulary used to describe (a particular view of)
some domain
 An explicit specification of the intended meaning of the
vocabulary.
 almost always includes how concepts should be classified

Constraints capturing additional knowledge about the
domain
Ideally, an ontology should:
 Capture a shared understanding of a domain of interest
 Provide a formal and machine manipulable model of the
domain
– 36 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Example Ontology
Vocabulary and meaning (“definitions”)

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Elephant is a concept whose members are a kind of animal
Herbivore is a concept whose members are exactly those
animals who eat only plants or parts of plants
Adult_Elephant is a concept whose members are exactly those
elephants whose age is greater than 20 years
Background knowledge/constraints on the domain (“general
axioms”)
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
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– 37 –
Adult_Elephants weigh at least 2,000 kg
All Elephants are either African_Elephants or Indian_Elephants
No individual can be both a Herbivore and a Carnivore
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Where are ontologies used?
e-Science, e.g., Bioinformatics

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The Gene Ontology
The Protein Ontology (MGED)
“in silico” investigations relating theory and data
Medicine

Terminologies
Databases
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
Integration
Query answering
User interfaces
Linguistics
The Semantic Web
– 38 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Why Ontology Reasoning?
Given key role of ontologies in many applications, it is essential
to provide tools and services to help users:

Design and maintain high quality ontologies, e.g.:
 Meaningful — all named classes can have instances
 Correct — captured intuitions of domain experts
 Minimally redundant — no unintended synonyms
 Richly axiomatised — (sufficiently) detailed descriptions

Answer queries over ontology classes and instances, e.g.:
 Find more general/specific classes
 Retrieve individuals/tuples matching a given query

– 39 –
Integrate and align multiple ontologies
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Why Decidable Reasoning?
OWL is an W3C standard DL based ontology language

OWL constructors/axioms restricted so reasoning is decidable
Consistent with Semantic Web's layered architecture




XML provides syntax transport layer
RDF(S) provides basic relational language and simple ontological
primitives
OWL provides powerful but still decidable ontology language
Further layers (e.g. SWRL) will extend OWL
 Will almost certainly be undecidable
W3C requirement for “implementation experience”
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– 40 –
“Practical” decision procedures
Several implemented systems
Evidence of empirical tractability
CSCE 771 Spring 2013
Why Correct Reasoning?
Need to have high level of confidence in reasoner

Most interesting/useful inferences are those that were
unexpected

Likely to be ignored/dismissed if reasoner known to be
unreliable
Many realistic web applications will be agent ↔
agent

– 41 –
No human intervention to spot glitches in reasoning
CSCE 771 Spring 2013
Use a (Description) Logic
OWL DL based on SHIQ Description Logic

In fact it is equivalent to SHOIN(Dn) DL
OWL DL Benefits from many years of DL research


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Well defined semantics
Formal properties well understood (complexity, decidability)
Known reasoning algorithms
Implemented systems (highly optimised)
In fact there are three “species” of OWL (!)


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– 42 –
OWL full is union of OWL syntax and RDF
OWL DL restricted to First Order fragment (¼ DAML+OIL)
OWL Lite is “simpler” subset of OWL DL (equiv to SHIF(Dn))
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
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
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– 43 –
Restricted form of DL concrete domains
CSCE 771 Spring 2013
RDFS Syntax
E.g., Person u 8hasChild.(Doctor t 9hasChild.Doctor):
<owl:Class>
<owl:intersectionOf rdf:parseType=" collection">
<owl:Class rdf:about="#Person"/>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasChild"/>
<owl:toClass>
<owl:unionOf rdf:parseType=" collection">
<owl:Class rdf:about="#Doctor"/>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasChild"/>
<owl:hasClass rdf:resource="#Doctor"/>
</owl:Restriction>
</owl:unionOf>
</owl:toClass>
</owl:Restriction>
</owl:intersectionOf>
</owl:Class>
– 44 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Ontologies / Knowledge Bases
OWL ontology equivalent to a DL Knowledge Base
OWL ontology consists of a set of axioms and facts

Note: an ontology is usually thought of as containing only
Tbox axioms (schema)---OWL is non-standard in this
respect
Recall that a DL KB K is a pair hT ,Ai where


– 47 –
T is a set of “terminological” axioms (the Tbox)
A is a set of “assertional” axioms (the Abox)
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
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
– 48 –

“Definitions” C v D or C ´ D where C is a concept name

General Concept Inclusion axioms (GCIs) where C may be
complex
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Ontology Facts / Abox Axioms
Note: using nominals (e.g., in SHOIN), can reduce
Abox axioms to concept inclusion axioms


– 49 –
equivalent to
equivalent to
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Recent Developments
Algorithms for NExpTime logics such as SHOIQ
Increased expressive power (roles, keys, etc.)
Graph based algorithms for Polynomial logics
Automata based algorithms
– 57 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Current Research
Extending Description Logics


Complex roles, finite domains, concrete domains, keys,
e-connections, …
Future OWL extensions (e.g., with “rules”)
Integrating with other logics/systems

E.g., Answer Set Programming
Alternative reasoning techniques

Automata based algorithms
Translation into datalog

Graph based algorithms (for sub ALC languages)

– 58 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Current Research
Improving Scalability


Very large ontologies
Very large numbers of individuals
Other reasoning tasks (non-standard inferences)

Matching, LCS, explanation, querying, …
Implementation of tools and Infrastructure



More expressive languages (such as SHOIN)
New algorithmic techniques
Tools to support for large scale ontological engineering
 Editing, visualisation, etc.
– 59 –
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
CSCE 771 Spring 2013
Summary
DLs are a family of logic based Knowledge
Representation formalisms

Describe domain in terms of concepts, roles and
individuals
An Ontology is an engineering artefact consisting of:


A vocabulary of terms
An explicit specification their intended meaning
Ontologies play a key role in many applications

– 60 –
e-Science, Medicine, Databases, Semantic Web, etc.
CSCE 771 Spring 2013
Summary
Reasoning is important

Essential for design, maintenance and deployment of
ontologies
Reasoning support based on DL systems


Tableaux decision procedures
Highly optimised implementations
Many exciting challenges remain
– 61 –
CSCE 771 Spring 2013