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Fuzzy DL, Fuzzy SWRL, Fuzzy Carin (report from visit to Athens)

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Tableaux algorithms can be extended to deal with fuzziness ... Fuzzy Carin adds fuzziness to Carin. (decidable) Fuzzy Carin. END ... – PowerPoint PPT presentation

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Title: Fuzzy DL, Fuzzy SWRL, Fuzzy Carin (report from visit to Athens)


1
Fuzzy DL, Fuzzy SWRL, Fuzzy Carin(report from
visit to Athens)
  • M.Vacura
  • VŠE Praha
  • (used materials by G.Stoilos, NTU Athens)

2
Description Logics
  • Concept and Role Oriented
  • Concepts (Unary) Man, Tall, Human, Brain
  • Roles (Binary) hasChild, hasColor
  • Individuals John, Object1, Italy, Monday

3
Concepts
  • Concepts
  • Universal ?
  • Empty ?
  • Atomic/primitive concepts (concept names)
  • Complex concepts (terms)
  • Concept Constructors
  • ?, ?, ?, ?, ?, ?, ?
  • ( Animal ? Rational)

4
Axioms
  • Concept Axioms T box (terminology)
  • Woman ? Person ? Female
  • Parent ? Person ? ?hasChild.Person
  • Role Axioms R box
  • hasSon ? hasChild
  • Trans(hasOffspring)
  • Instance Axioms (Assertions) A box
  • Bob Parent
  • (Bob,Helen)hasChild

5
Typology of DLs
  • Constructors of Description logics AL
  • Negation ? A (A primitive)
  • Conjunction (A ? B)
  • Universal quantification ?R.C
  • Limited existential quantification ?R.?

6
Typology of DLs
  • Constructors of Description logics ALU
  • (A ? B) (disjunction)
  • Constructors of Description logics ALE
  • ?R.C (full existencial quantification)
  • Constructors of Description logics ALN
  • (?n C) , (?n C) (numerical restriction)
  • Constructors of Description logics ALC
  • (? A) (full negation)

7
Typology of DLs
  • Description logics S
  • ALCR ALC transitive roles axioms.
  • Trans(hasOffspring)
  • Description logics SH
  • SH S role hiearchy axioms.
  • hasSon ? hasChild
  • Description logics SHf
  • SHf SH role functional axioms.
  • Func(R)

8
Typology of DLs
  • Description logics SHO
  • SHO SH nominal axioms.
  • C ? a
  • Description logics SHOI
  • SHO SH inverse role axioms.
  • Description logics SHOIN
  • SHOIN SHOI numerical restrictions.

9
Typology of DLs
  • Description logics SHOIQ
  • SHOIQ SHOI qualified numerical restrictions.
  • Description logics SROIQ
  • SROIQ SHOIQ extended role axioms
  • disjoint roles, reflexive and irreflexive roles,
    negated role assertions (A box), complex role
    inclusion axioms, local reflexivity axioms.

10
Important DLs
  • ALC base DL
  • SHOIN OWL DL
  • SROIQ OWL DL 1.1
  • (Support for datatypes)

11
Uncertainty and Applications
  • Several Applications from Industry and Academic
    face uncertain imprecision
  • Multimedia Processing (Image Analysis and
    Annotation)
  • Medical Diagnosis
  • Geospatial Applications
  • Information Retrieval
  • Sensor Readings
  • Decision Making

12
Uncertainty
  • Imprecision (Possibility Theory)
  • Vagueness (Fuzzy Set Theory)
  • Randomness (Probability Theory)

13
Fuzzy Set Theory
  • An object belongs to a set to a degree between 0
    and 1. (membership degree).
  • Tall(George)0.7
  • A pair of objects belongs to a relation to a
    degree between 0 and 1. (membership degree).
  • Far(Prague,Paris)0.6

14
Fuzzy Set Theoretic Operations
  • Complement c(x)
  • c(x)1-x
  • Intersection t(x,y)
  • t(x,y)min(x,y), t(x,y)max(0,xy-1)
  • t-norm Godel, Lukasiewicz
  • Union u(x,y)
  • u(x,y)max(x,y), u(x,y)min(1,xy)
  • s-norm Godel, Lukasiewicz
  • Implication J(x,y)
  • J(x,y)max(1-x,y), J(x,y)min(1,1-xy)
  • Kleene-Dienes, Lukasiewicz

15
Fuzzy DLs
  • Syntax Extensions
  • A box
  • Fuzzy assertions DLAssertion ?, ?, gt, lt 0,1
  • GeorgeTall ? 0.7,
  • (Prague, Paris)Far ? 0.6

16
Complex concepts
  • BobTall ? 0.8
  • BobAthletic ? 0.6
  • Bob(Athletic ? Tall) ? t(0.6,0.8)

17
Reasoning
  • Usually DL Reasoning is done with tableaux
    algorithms.
  • Tableaux algorithms can be extended to deal with
    fuzziness
  • NTU Athens - Implementation for fKD-SHIN
  • Reasoner FIRE

18
Future
  • Fuzzy T box
  • ltC ? Dgt ? 0,6
  • Fuzzy R box
  • ltR ? Sgt ? 0,3

19
Fuzzy SWRL
20
SWRL
  • A Semantic Web Rule Language Combining OWL and
    RuleML
  • (undecidable)
  • RuleML Rule Markup Language
  • (www.ruleml.org)

21
Fuzzy SWRL
  • OWL A box
  • OWL asserions can include a specification of the
    degree (a truth value between 0 and 1) of
    confidence with which we assert that an
    individual (resp. pair of individuals) is an
    instance of a given class (resp.property).
  • RuleML
  • atoms can include a weight (a truth value
    between 0 and 1) that represents the importance
    of the atom in a rule.

22
Fuzzy SWRL
  • Fuzzy rule assertions
  • antecedent ? consequent
  • parent(?x, ?p) ? Happy(?p) ? Happy(?x) 0.8,
  • EyebrowsRaised(?a)0.9 ? MouthOpen(?a)0.8 ?
    Happy(?a)

23
Fuzzy Carin
24
Fuzzy Carin
  • Carin combines the description logic ALCNR with
    Horn Rules.
  • Fuzzy Carin adds fuzziness to Carin.
  • (decidable)

25
Fuzzy Carin
26
END
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