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

Fuzzy DL, Fuzzy SWRL, Fuzzy Carin (report from visit to Athens). M.Vacura VŠE Praha (used materials by G . Stoilos , NTU Athens). Description Logics. Concept and Role Oriented Concepts (Unary): Man, Tall, Human, Brain Roles (Binary): hasChild, hasColor

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

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  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,x+y-1) • t-norm Godel, Lukasiewicz • Union: u(x,y) • u(x,y)=max(x,y), u(x,y)=min(1,x+y) • s-norm Godel, Lukasiewicz • Implication: J(x,y) • J(x,y)=max(1-x,y), J(x,y)=min(1,1-x+y) • Kleene-Dienes, Lukasiewicz

  15. Fuzzy DLs • Syntax Extensions • A box • Fuzzy assertions: DLAssertion {, , >, <} [0,1] • George:Tall  0.7, • (Prague, Paris):Far  0.6

  16. Complex concepts • Bob:Tall  0.8 • Bob:Athletic  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 • <C D>  0,6 • Fuzzy R box • <R S>  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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