PowerPointPrsentation

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Logics one, no one and one hundred
thousand Juri De Coi L3S Research
Seminar Hannover, 09-06-2006
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Please, forgive me!
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Please, forgive me! Please, help me!
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Why did I do what I did?
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Why did I do what I did?

• WP0 State of the art investigation.
• Description Logic-based Policy Specification
  Languages (KAoS, REI)
• Logic Programming-based Policy Specification
  Languages (PeerTrust, Protune)

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Why did I do what I did?

• WP0 State of the art investigation.
• Description Logic-based Policy Specification
  Languages (KAoS, REI)
• Logic Programming-based Policy Specification
  Languages (PeerTrust, Protune)
• WP1 Study of DL and LP.

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Why did I do what I did?

• WP0 State of the art investigation.
• Description Logic-based Policy Specification
  Languages (KAoS, REI)
• Logic Programming-based Policy Specification
  Languages (PeerTrust, Protune)
• WP1 Study of DL and LP.
• WP2 Mapping DL and LP to a common formalism.

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Grosof et al., Description Logic Programs
Combining Logic Programs with Description Logic
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Description of Work

• WP0 State of the art investigation.
• Description Logic-based Policy Specification
  Languages (KAoS, REI)
• Logic Programming-based Policy Specification
  Languages (PeerTrust, Protune)
• WP1 Study of DL, LP and FOL.
• WP2 Mapping DL and LP to FOL (as far as
  possible).

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Description of Work

• WP0 State of the art investigation.
• Description Logic-based Policy Specification
  Languages (KAoS, REI)
• Logic Programming-based Policy Specification
  Languages (PeerTrust, Protune)
• WP1 Study of DL, LP and FOL.
• WP2 Mapping DL and LP to FOL (as far as
  possible).
• WP3 Identify the set of features we are
  interested in.? Identify the sustainable overhead.

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Description of Work

• WP0 State of the art investigation.
• Description Logic-based Policy Specification
  Languages (KAoS, REI)
• Logic Programming-based Policy Specification
  Languages (PeerTrust, Protune)
• WP1 Study of DL, LP and FOL.
• WP2 Mapping DL and LP to FOL (as far as
  possible).
• WP3 Identify the set of features we are
  interested in ? Identify the sustainable overhead.

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WP1 Study of DL, LP and FOL.

• First-order Logic
  
  
  
  
  
• Description Logic
• Logic Programming
  
  

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WP1 Study of DL, LP and FOL.

• Propositional logic
• First-order Logic (Horn-clause Logic, Definite
  Horn-clause Logic, Equality-free Horn-clause
  Logic, Datalog Horn-clause Logic, def-Horn Logic,
  Description Horn Logic)
• Description Logic (l, lh, lb)
• Logic Programming (Definite Logic Programming,
  Equality-free Logic Programming, Datalog,
  def-Logic Programming, Description Logic
  Programming, Rules with Contextually Scoped
  Negation)
• Resource Description Framework - RDF
• Web Ontology Language - OWL (Lite, Description
  Logic - DL, Full)
• Semantic Web Rule Language - SWRL
• Al-log

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Propositional Logic

• Propositional variables xi (a denumerable set)
• Negation ?
• Conjunction ?
• Disjunction ?
• Implication ?
• EX (x1 ? x2) ? (?x1 ? x2)

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First-order Logic

• n-ary predicates Pni(_, _, ... _) (a denumerable
  set)
• Individual constants ai (a denumerable set)
• Individual variables xi (a denumerable set)
• Universal quantifier ?
• Existential quantifier ?
• EX ?x1(P2,1(a1, x1) ? P2,2(x2, a2)) ?
• ?x2(?P2,1(x1, a2) ? P2,2(a1, x2))

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Open issues

• What are parameters?

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Open issues

• What are parameters?
• FOL does not deal with equality
• FOL does not deal with function symbols

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Grosof et al., Description Logic Programs
Combining Logic Programs with Description Logic
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Description Logics (I)
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Description Logics (I)
Concept
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Description Logics (I)
Concept Role
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Description Logics (I)
Concept Role Instance
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Description Logics (II)

• Atomic concept A (default concepts ? and ?)

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Description Logics (II)

• Atomic concept A (default concepts ? and ?)
• Negation ?C
• Intersection C ? D
• Union C ? D
• (Full) existential quantification ?R.C

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Description Logics (II)

• Atomic concept A (default concepts ? and ?)
• Negation ?C
• Intersection C ? D
• Union C ? D
• (Full) existential quantification ?R.C
• Number restriction (cardinality constraint)
• n R.C
• n R.C

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Description Logics (II)

• Atomic concept A (default concepts ? and ?)
• Negation ?C
• Intersection C ? D
• Union C ? D
• (Full) existential quantification ?R.C
• Number restriction (cardinality constraint)
• n R.C
• n R.C
• Value restriction ?R.C

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Open issue

• Do people without children belong to the Concept
  of "people whose children are only female"
  (?hasChild.Female)?

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Open issue

• Do people without children belong to the Concept
  of "people whose children are only female"
  (?hasChild.Female)?
• Grosof et al. yes

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Open issue

• Do people without children belong to the Concept
  of "people whose children are only female"
  (?hasChild.Female)?
• Grosof et al. yes
• Baader et al. no (?)

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Description Logics (III)

• Atomic role R
• Intersection R ? S
• Inverse role R-
• Transitive closure R
• Concept assertion aC
• Role assertion lta, bgtR

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Description Logics (IV)
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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S

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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S
• Symmetrical property
• Transitive property
• Functional property
• Inverse functional property
• C is range of R
• C is domain of R

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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S
• Symmetrical property R- ? R
• Transitive property
• Functional property
• Inverse functional property
• C is range of R
• C is domain of R

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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S
• Symmetrical property R- ? R
• Transitive property R ? R
• Functional property
• Inverse functional property
• C is range of R
• C is domain of R

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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S
• Symmetrical property R- ? R
• Transitive property R ? R
• Functional property ? ? 1 R.?
• Inverse functional property
• C is range of R
• C is domain of R

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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S
• Symmetrical property R- ? R
• Transitive property R ? R
• Functional property ? ? 1 R.?
• Inverse functional property ? ? 1 R-.?
• C is range of R
• C is domain of R

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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S
• Symmetrical property R- ? R
• Transitive property R ? R
• Functional property ? ? 1 R.?
• Inverse functional property ? ? 1 R-.?
• C is range of R ?R.? ? C (according to Grosof
  et al. ? ? ?R.C)
• C is domain of R

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Description Logics (IV)

• Inclusion axiom
• C ? D
• R ? S
• Symmetrical property R- ? R
• Transitive property R ? R
• Functional property ? ? 1 R.?
• Inverse functional property ? ? 1 R-.?
• C is range of R ?R.? ? C (according to Grosof
  et al. ? ? ?R.C)
• C is domain of R ?R-.? ? C (according to Grosof
  et al. ? ? ?R-.C)

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Resource Description Framework (RDF) and RDF
Schema (RDFS)
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Resource Description Framework (RDF) and RDF
Schema (RDFS)

• Support for
• definition of atomic Concepts/Roles (? is called
  rdfsResource)
• Concept/Role assertions
• Concept/Role inclusion axioms
• domain/range specification
• Open issue
• Unique-ID assumption?

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Additional features

• Facilities to deal with
• common data-types (the predefined Concept
  rdfsLiteral)
• collections

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RDF(S) Example

• lta, bgt R
• ltrdfStatementgt
• ltrdfsubject rdfresource"a" /gt
• ltrdfpredicate rdfresource"R" /gt
• ltrdfobject rdfresource"b" /gt
• lt/rdfStatementgt

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RDF(S) Example

• ltrdfStatementgt
• ltrdfsubject rdfresource"R" /gt
• ltrdfpredicate rdfresource"R" /gt
• ltrdfobject rdfresource"R" /gt
• lt/rdfStatementgt

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RDF(S) Example

• ltrdfStatement rdfID"S"gt
• ltrdfsubject rdfresource"S" /gt
• ltrdfpredicate rdfresource"R" /gt
• ltrdfobject rdfresource"R" /gt
• lt/rdfStatementgt

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Web Ontology Language (OWL)

• Extension of RDF(S)
• Available in three flavours (Lite, Description
  Logic - DL, Full)
• OWL expressiveness
• varies according to the chosen flavour
• can reach (and pass) the one of the
  above-described DL languages

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Web Ontology Language (OWL)

• Extension of RDF(S)
• Available in three flavours (Lite, Description
  Logic - DL, Full)
• OWL expressiveness
• varies according to the chosen flavour
• can reach (and pass) the one of the
  above-described DL languages
• Additional features
• No Role intersection
• No unique-ID assumption
• Two kinds of Roles
  (owlDatatypeProperty and
  owlObjectProperty)

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Logic Programming
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Logic Programming

• n-ary predicates Pni(_, _, ... _)
• n-ary functions Fni(_, _, ... _)
• Constants ai
• Variables xi

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Logic Programming

• n-ary predicates Pni(_, _, ... _)
• n-ary functions Fni(_, _, ... _)
• Constants ai
• Variables xi
• Negation-as-failure

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Logic Programming

• n-ary predicates Pni(_, _, ... _)
• n-ary functions Fni(_, _, ... _)
• Constants ai
• Variables xi
• Negation-as-failure
• P0
• ? Pa1, ... Pan, Pb1, ... Pbm with m,n0 and
  mngt0
• P0 ? Pa1, ... Pan, Pb1, ... Pbm with m,n0 and
  mngt0

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Open issues (among others)

• What is an atom?

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Open issues (among others)

• What is an atom?
• What are procedural attachments?

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WP2 Mapping DL to FOL (?)

• cf. File

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WP2 Mapping LP to FOL (??)
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WP2 Mapping LP to FOL (??)

• (i) P0
• (ii) ? P1, ... Pn with ngt0
• (iii) P0 ? P1, ... Pn with ngt0

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WP2 Mapping LP to FOL (??)

• (i) P0
• (ii) ? P1, ... Pn with ngt0
• (iii) P0 ? P1, ... Pn with ngt0
• Let x1, ... xn be the variables appearing in
  (iii) (resp. (ii) or (i))
• (iii) ?x1, ... xn (P0 ? P1 ? ... Pn) with ngt0

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WP2 Mapping LP to FOL (??)

• (i) P0
• (ii) ? P1, ... Pn with ngt0
• (iii) P0 ? P1, ... Pn with ngt0
• Let x1, ... xn be the variables appearing in
  (iii) (resp. (ii) or (i))
• (iii) ?x1, ... xn (P0 ? P1 ? ... Pn) with ngt0
• (iii') ?x1, ... xn (P0 ? ?P1 ? ... ?Pn)

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WP2 Mapping LP to FOL (??)

• (i) P0
• (ii) ? P1, ... Pn with ngt0
• (iii) P0 ? P1, ... Pn with ngt0
• Let x1, ... xn be the variables appearing in
  (iii) (resp. (ii) or (i))
• (iii) ?x1, ... xn (P0 ? P1 ? ... Pn) with ngt0
• (iii') ?x1, ... xn (P0 ? ?P1 ? ... ?Pn)
• (ii) ?x1, ... xn (?P0 ? ... ?Pn)
• (i) ?x1, ... xn P0

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Further work

• Understand what I did not understand
• Map what I did not map
• inverse role
• transitive closure
• RTF collections
• RTF data-type facilities
• owlDatatypeProperty and owlObjectProperty
• lack of unique-ID assumption
• Extend the set of considered logic languages
• WP3 Identify the set of features we are
  interested in ? Identify the sustainable overhead

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