Department of Computer Science

1
Department of Computer Science Engineering
University of California, San DiegoCSE-291
Ontologies in Data IntegrationSpring 2003

• Bertram Ludäscher
• LUDAESCH_at_SDSC.EDU

2
Outline

• Wrapping up last week
• What is a representation?
• Thesauri, Topic Maps
• Predicate Logic Primer
• Description logics
• RDF RDF Schema
• F-logic
• Topic Selection
• Special thanks
• Alexander Maedche, Steffen Staab
• ECAI2002 Tutorial on Ontologies

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Ontologies For What?

• Lack of a shared understanding leads to poor
  communication
  
• People, organizations and software
  systems
  
• must communicate between and among
• themselves
• Disparate modeling paradigms, languages and
  software tools limit
  
• Interoperability
• Knowledge sharing reuse

Uschold, Gruninger, 96
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Origin and History (I)

• Ontology ....
• a philosophical discipline, 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 is being?
• What are the features common to all beings?

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Origin and History (II)
Humans require words (or at least symbols) to
communicate efficiently. The mapping of words to
things is only indirect possible. We do it by
creating concepts that refer to things.
The relation between symbols and things has been
described in the form of the meaning triangle
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Origin and History (III)
In recent years ontologies have become a hot
topic of interest. Here, an ontology refers to
an engineering artifact It is constituted by a
specific vocabulary used to describe a certain
reality, plus a set of explicit assumptions rega
rding the intended meaning of the vocabulary.
Thus, ontologies describe a formal partial speci
fication of a specific domain
Shared understanding of a domain of interest
Formal and machine executeable model of a domain
of interest
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Human and machine communication (I)
Maedche et al., 2002
...
Machine Agent 1
Human Agent 2
Machine Agent 2
Human Agent 1
exchange symbol, e.g. via nat. language
exchange symbol, e.g. via protocols
Ontology Description
Symbol
JAGUAR
Formal Semantics
Formal models
Internal models
commit
commit
Concept
Meaning Triangle
MA1
MA2
HA2
HA1
commit
Ontology
commit
a specific domain, e.g. animals
Things
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Ontology Natural Language

• It is important to emphasize that there is a mn
  relationship between words and concepts
  
• This means practically
• different words may refer to the same concept
• a word may refer to several concepts
• Ontologies languages should provide means for
  making this difference explicit.

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Example
Ontology C c1,c2, c3, R r1, HC(c2,c1),
r1(c2,c3),

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Ontology vs. Knowledge Bases

• There is no clear separation between ontology and
  knowledge base
  
• Example
• Often it remains a modeling decision if something
  is modeled as concept or as instance. In many
  applications meta-modeling means are required.

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Types of Ontologies (I)
Guarino, 98
describe very general concepts like space, time,
event, which are independent of a particular
problem or domain. It seems reasonable to have
unified top-level ontologies for large
communities of users.
describe the vocabulary related to a generic
domain by specializing the concepts introduced in
the top-level ontology.
describe the vocabulary related to a generic task
or activity by specializing the top-level
ontologies.
These are the most specific ontologies. Concepts
in application ontologies often correspond to
roles played by domain entities while performing
a certain activity.
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Ontologies and their Relatives (I)

• There are many relatives around
• Controlled vocabularies, thesauri and
  classification systems available in the WWW, see
  http//www.lub.lu.se/metadata/subject-help.html
  
• Classification Systems (e.g. UNSPSC, Library
  Science, etc.)
  
• Thesauri (e.g. Art Architecture, Agrovoc,
  etc.)
  
• Lexical Semantic Nets
• WordNet, see http//www.cogsci.princeton.edu/wn/
  
• EuroWordNet, see http//www.hum.uva.nl/ewn/
• Topic Maps, http//www.topicmaps.org (e.g. used
  within knowledge management applications)
  
• In general it is difficult to find the border
  line!

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Ontologies and their Relatives (II)
General logical constraints
Formal Is-a
Thesauri
Frames
Catalog / ID
Informal Is-a
Formal Instance
Value Restric- tions
Terms/ Glossary
Axioms Disjoint Inverse Relations, ...
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Some Ontologies (and Friends) in Action

• (coming soon to a project near you)

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GEON Architecture
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SMART (Meta)data I Logical Data Views
Adoption of a standard (meta)data model wrap
data sets into unified virtual views
Source NADAM Team (Boyan Brodaric et al.)
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SMART Metadata II Multihierarchical Rock
Classification for Thematic Queries (GSC)
or Taxonomies are not only for biologists ...
Genesis
Fabric
Composition
Texture
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SMART Metadata III Source Contextualization
Ontology Refinement
Biomedical Informatics Research Network http/
/nbirn.net
Focused GEON ontology working meeting
last week ... (GEON, SCEC/KR, GSC, ESRI)
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EcoCyc
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Gene Ontology http//www.geneontology.org
a dynamic controlled vocabulary that can be
applied to all eukaryotes Built by the community
for the community. Three organising principles
Molecular function, Biological process, Cellular
component Isa and Part of taxonomy but not good
! 10,000 concepts Lightweight ontology, Poor se
mantic rigour. Ok when small and used for
annotation. Obstacle when large, evolving and
used for mining.
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Controlled vocabulary

• AGROVOC Agricultural Vocabulary

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Thesauri

• AAT Art Architecture Thesaurus

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Ontologies - Some Examples

• General purpose ontologies
• WordNet / EuroWordNet, http//www.cogsci.princeton
  .edu/wn
  
• The Upper Cyc Ontology, http//www.cyc.com/cyc-2-1
  /index.html
  
• IEEE Standard Upper Ontology, http//suo.ieee.org/
  
  
• Domain and application-specific ontologies
• RDF Site Summary RSS, http//groups.yahoo.com/grou
  p/rss-dev/files/schema.rdf
  
• UMLS, http//www.nlm.nih.gov/research/umls/
• KA2 / Science Ontology, http//ontobroker.semantic
  web.org/ontos/ka2.html
  
• RETSINA Calendering Agent, http//ilrt.org/discove
  ry/2001/06/schemas/ical-full/hybrid.rdf
  
• AIFB Web Page Ontology, http//ontobroker.semantic
  web.org/ontos/aifb.html
  
• Web-KB Ontology, http//www-2.cs.cmu.edu/afs/cs.cm
  u.edu/project/theo-11/www/wwkb/
  
• Dublin Core, http//dublincore.org/
• Meta-Ontologies
• Semantic Translation, http//www.ecimf.org/contrib
  /onto/ST/index.html
  
• RDFT, http//www.cs.vu.nl/borys/RDFT/0.27/RDFT.rd
  fs
  
• Evolution Ontology, http//kaon.semanticweb.org/ex
  amples/Evolution.rdfs
  

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Ontology Representation

• What is a representation?

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Ontology Representation Languages

• Machines need communication with formal content
  to restrict meaning
  
• What makes a language formal?
• model theory (1st order predicate logic)
• proof theory (Gentzen calculus)
• But also
• conventions (e.g. Java)

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What makes a language suitable?

• For machine communication
• ? model theory ?
• ? proof theory
• ? tracktability
• ? strong conventions of use
• ? human readable names ?

• For human communication
• ? strong conventions of use ?
• ? human readable names ?
• ? natural primitives ?

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Representation Paradigms (incomplete)
TopicMaps
Thesauri
Taxonomies
Ontologies
Semantic Nets
extended ER-Modell
Predicate Logics /Description Logics
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Thesaurus
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Thesauri
similarTo
Fruit
Vegetable
Example
NarrowerTerm
Orange
Apfelsine (german)
synonymWith
Graph with labels edges (similar, nt, bt,
synonym) Fixed set of edge labels (aka relations
)
no instances
Well known in library science
cf. terminologies / classifications (Dewey)
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(No Transcript)
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Topic Maps are ...

• Standardized ISO/IEC 132502000
• ISO standard published Jan. 2000
• enabling standard to describe knowledge
  structures,electronic indices, classification
  schemes, ...
  
• Web enabled
• XML Topic Maps (XTM) are ready to use
• Designed to
• manage the info glut
• build valuable information networks above any
  kind of resources / data objects
  
• enable the structuring of unstructured information

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Back-of-the-Book Index British Virgin Islands
Gorda Sound see North Sound Little Dix Bay ......
.............. 89 North Sound ...................
.... 90 Road Harbour see also Road Town ... 73 R
oad Town ...................... 69,71Spanish
Town ................... 81,82
Tortola ........................... 67Virgin
Gorda ...................... 77
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Back-of-the-Book Index British Virgin Islands
Gorda Sound see North Sound Little Dix Bay ......
.............. 89 North Sound ...................
.... 90 Road Harbour see also Road Town ... 73 R
oad Town ...................... 69,71Spanish
Town ................... 81,82
Tortola ........................... 67Virgin
Gorda ...................... 77
Topics
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Back-of-the-Book Index British Virgin Islands
Gorda Sound see North Sound Little Dix Bay ......
.............. 89 North Sound ...................
.... 90 Road Harbour see also Road Town ... 73 R
oad Town ...................... 69,71Spanish
Town ................... 81,82
Tortola ........................... 67Virgin
Gorda ...................... 77
Occurrences
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Back-of-the-Book Index British Virgin Islands
Gorda Sound see North Sound Little Dix Bay ......
.............. 89 North Sound ...................
.... 90 Road Harbour see also Road Town ... 73 R
oad Town ...................... 69,71Spanish
Town ................... 81,82
Tortola ........................... 67Virgin
Gorda ...................... 77
Different topic classes
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Back-of-the-Book Index British Virgin Islands
Gorda Sound see North Sound Little Dix Bay ......
.............. 89 North Sound ...................
.... 90 Road Harbour see also Road Town ... 73 R
oad Town ...................... 69,71Spanish
Town ................... 81,82
Tortola ........................... 67Virgin
Gorda ...................... 77
Different occurrences classes
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Back-of-the-Book Index British Virgin Islands
Gorda Sound see North Sound Little Dix Bay ......
.............. 89 North Sound ...................
.... 90 Road Harbour see also Road Town ... 73 R
oad Town ...................... 69,71Spanish
Town ................... 81,82
Tortola ........................... 67Virgin
Gorda ...................... 77
Multiple topic names
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Back-of-the-Book Index British Virgin Islands
Gorda Sound see North Sound Little Dix Bay ......
.............. 89 North Sound ...................
.... 90 Road Harbour see also Road Town ... 73 R
oad Town ...................... 69,71Spanish
Town ................... 81,82
Tortola ........................... 67Virgin
Gorda ...................... 77
Association
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Topics Computerized Subjects
Topic classes
Topics
Subject
Subject
Subject
Subject
Subject
Subject
Subject
Resources
SurfBVI
BVI Welcome
CaribNet
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Occurrences
Topics
Occurrences
Occurrenceclasses
Resources
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Occurrences
Topics
Occurrences
Occurrenceclasses
Resources
SurfBVI
BVI Welcome
CaribNet
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Associations
Association classes
Associations
Topics
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Associations
Association classes
Associations
Topics
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Class Hierarchies
Topic classes
Topics
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Class Hierarchies
Super-classes
Sub-classes
Topics
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Scopes
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Scopes
Scopes
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Scopes
Scopes
Names EnglishDeutsch
SurfBVI
BVI Welcome
CaribNet
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Scopes
Scopes
Names EnglishDeutsch
Occurrences PublicConfidential
SurfBVI
BVI Welcome
CaribNet
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Scopes
Scopes
Associations GeographyPolitics
Names EnglishDeutsch
Occurrences PublicConfidential
SurfBVI
BVI Welcome
CaribNet
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Scope Examples English, Public, Politics
Scopes
Associations GeographyPolitics
Geo Containment
Political Dependency
Names EnglishDeutsch
Article
Occurrences PublicConfidential
Map
Image
SurfBVI
BVI Welcome
CaribNet
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In-/Semi-formal approaches Topic Maps, Thesauri

• Advantages
• Capture a lot of modeling experiences
• Intuitive
• Interesting primitives that are not available in
  other approaches (TM)

• Disadvantages
• No characterization independent from particular
  implementation
  
• May be misinterpreted (TM) / few primitives
  (Thesauri)
  

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Common errors about ontology representation
languages

• AI peoples errors
• it is good if it is formal
• it is good if someone with a logic background
  may easily use it
  
• it is good if the language allows everything

• Engineers errors
• it works in my application, thus it is good
• who needs formality anyway?
• it did not work when I looked at it 10 years
  ago
  

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Review/Introduction(Classical) First-order
Predicate LogicShort FO or PL1
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But first Propositional Logic Syntax
propositional logic (or "propositional ca
lculus") A system of symbolic logic using symbols
to stand for whole propositions and logical
connectives. Propositional logic only considers
whether a proposition is true or false. In
contrast to predicate logic, it does not consider
the internal structure of propositions.
http//wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?propo
sitionallogic

• propositions (no internal structure) can be
  assigned a truth-value
  
• either true or false (classical 2-valued logic
  tertium non datur)
  
• Logical symbols
• conjunction ?, disjunction ?, negation ?,
• implication ?, equivalence ?, parentheses ? ?
• Non-logical symbols
• propositional variables p, q, r, ...
• signature set of propositional variables ? p,
  q, r, ...
  
• Formation rules for well-formed formulas (wff)
• an atomic formula (propositional variable) is a
  formula
  
• if F, G are formulas, so are
• F?G, F ? G, ? F, F?G , F?G, ? F ?

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Propositional Logic Semantics

• An interpretation I over a signature ? is a
  mapping
  
• I ? ? true, false , associating a truth
  value to every propositional variable
  
• Truth tables describe how to extend I from to
  composite formulas (Boolean Algebra)
  
• F?G, F ? G, ? F, F?G , F?G

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Boolean Algebra, Truth Tables
http//wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?two-v
aluedlogic
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Syntax of First-Order Logic (FO)

• Logical symbols
• ?, ?, ?, ?, ?, ? ?, ? (for all), ?
  (exists), ...
  
• Non-logical symbols A FO signature ? consists
  of
  
• constant symbols a,b,c, ...
• function symbols f, g, ...
• predicate (relation) symbols p,q,r, ....
• function and predicate symbols have an associated
  arity
  
• we can write, e.g., p/3, f/2 to denote the
  ternary predicate p and the function f with two
  arguments
  
• First-order variables x, y, ...
• Formation rules for terms
• constants and variables are terms
• if t_1,...t_k are terms and f is a k-ary function
  symbols then f(t_1,...,t_k) is a term
  

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Syntax of First-Order Logic (FO)

• Formation rules for formulas
• if t_1,...t_k are terms and p/k is a predicate
  symbol (of arity k) then p(t_1,...,p_k) is an
  atomic formula (short atom)
  
• all variable occurrences in p(t_1,..., t_k) are
  free
  
• if F,G are formulas and x is a variable, then
  the following are formulas
  
• F?G, F ? G, ? F, F?G , F?G, ? F ?,
• ?x F (for all x F(x,...) is true)
• ?x F (there exists x such that F(x,...) is
  true)
  
• the occurrences of a variable x within the scope
  of a quantifier are called bound occurrences.
  

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Examples

• ?x malePerson(x) ? person(x).
• malePerson(bill).
• child(marriage(bill,hillary),chelsea).
• Variable x
• Constants (0-ary function symbols) bill/0,
  hillary/0, chelsea/0
  
• Function symbols marriage/2
• Predicate symbols malePerson/1, person/1, child/2

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Semantics of Predicate Logic

• Let D be a non-empty domain (a.k.a. domain of
  discourse, universe). A structure is a pair I
  (D,I), with an interpretation I that maps ...
  
• each constant c to an element I(c)? D
• each predicate symbol p/k to a k-ary relation
  I(p) ? Dk,
  
• each function symbol f/k to a k-ary function
  I(f) Dk?D
  
• Given a structure I, and a set of variables X, a
  valuation is a mapping val X ? D, used to
  evaluate terms and formulas over a given FO
  signature ?
• with this term evaluation val(t) yields a domain
  element, and formula evaluation val(F) yields a
  truth value

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Example

• Formula F ?x malePerson(x) ? person(x).
• Domain D b, h, c, d, e
• Lets pick an interpretation I
• I(bill) b, I(hillary) h, I(chelsea) c
• I(person) b, h, c
• I(malePerson) b
• Under this I, the formula F evaluates to true.
• If we choose I like I but I(malePerson)
  b,d, then F evaluates to false
  
• Thus, I is a model of F, while I is not
• I F I / F

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FO Semantics (contd)

• F entails G (G is a logical consequence of F) if
  every model of F is also a model of G F
  G
  
• F is consistent or satisfiable if it has at least
  one model
  
• F is valid or a tautology if every interpretation
  of F is a model
  
• Proof Theory
• Let F,G, ... be FO sentences (no free variables).
  
  
• Then the following are equivalent
• F_1, ..., F_k G
• F_1 ? ... ? F_k ? G is valid
• F_1 ? ... ? F_k ? ? G is unsatisfiable
  (inconsistent)
  

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Proof Theory

• A calculus is formal proof system to establish
• F_1, ..., F_k G
• via formal (syntactic) derivations
• F_1, ..., F_k ... G, where the
  denotes allowed proof steps
  
• Examples
• Hilbert Calculus, Gentzen Calculus, Tableaux
  Calculus, Natural Deduction, Resolution, ...
  
• First-order logic is semi-decidable
• the set of valid sentences is recursively
  enumerable, but not recursive (decidable)
  
• Some inference engines
• http//www.semanticweb.org/inference.html

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Description LogicsDecidable Fragments of FO

• (aka terminological logics,member of concept
  languages)

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Formalism for Ontologies Description Logic

• DL definition of Happy Father
  (Example from Ian Horrocks, U
  Manchester, UK)

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Description Logic Statements as Rules

• Another syntax first-order logic in rule form
  (implicit quantifiers)
  
• happyFather(X) ?
• man(X), child(X,C1), child(X,C2), blue(C1),
  green(C2),
  
• not ( child(X,C3), poorunhappyChild(C3) ).
• poorunhappyChild(C) ?
• not rich(C), not happy(C).
• Note
• the direction ? is implicit here (sigh)
• see, e.g., Clarks completion in Logic
  Programming

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Description Logics

• Terminological Knowledge (TBox)
• Concept Definition (naming of concepts)
• Axiom (constraining of concepts)
• a mediators glue knowledge source
• Assertional Knowledge (ABox)
• the marked neuron in image 27
• the concrete instances/individuals of the
  concepts/classes that your sources export
  

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Querying vs. Reasoning

• Querying
• given a DB instance I ( logic interpretation),
  evaluate a query expression (e.g. SQL, FO
  formula, Prolog program, ...)
  
• boolean query check if I ? (i.e.,
  if I is a model of ?)
  
• (ternary) query (X, Y, Z) I ?
  (X,Y,Z)
  
• check happyFathers in a given database
• Reasoning
• check if I ? implies I ? for all
  databases I,
  
• i.e., if ? ?
• undecidable for FO, F-logic, etc.
• Descriptions Logics are decidable fragments
• concept subsumption, concept hierarchy,
  classification
  
• semantic tableaux, resolution, specialized
  algorithms

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Formalizing Glue KnowledgeDomain Map for
SYNAPSE and NCMIR
Domain Map labeled graph with concepts ("cla
sses") and roles ("associations") additional s
emantics expressed as logic rules
71
Source Contextualization DM Refinement
sources can register new concepts at the
mediator ...