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

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

• M.Vacura
• VŠE Praha
• (used materials by G.Stoilos, NTU Athens)

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Description Logics

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

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Concepts

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

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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

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Typology of DLs

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

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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)

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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)

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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.

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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.

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Important DLs

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

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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

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Uncertainty

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

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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

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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

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Fuzzy DLs

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

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Complex concepts

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

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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

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Future

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

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Fuzzy SWRL
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SWRL

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

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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.

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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)

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Fuzzy Carin
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Fuzzy Carin

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

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Fuzzy Carin
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END