Fuzzy DL Fuzzy SWRL Fuzzy Carin report from
- Slides: 26
Fuzzy DL, Fuzzy SWRL, Fuzzy Carin (report from visit to Athens) M. Vacura VŠE Praha (used materials by G. Stoilos, NTU Athens)
Description Logics l Concept and Role Oriented l l l Concepts (Unary): Man, Tall, Human, Brain Roles (Binary): has. Child, has. Color Individuals: John, Object 1, Italy, Monday
Concepts l Concepts: l l l Universal ⊤ Empty ⊥ Atomic/primitive concepts (concept names) Complex concepts (terms) Concept Constructors: l l , ⊔, ⊓, , ( Animal ⊓ Rational)
Axioms l Concept Axioms – T box (terminology) l l l Role Axioms – R box l l l Woman Person ⊓ Female Parent Person ⊓ has. Child. Person has. Son has. Child Trans(has. Offspring) Instance Axioms (Assertions) – A box l l Bob: Parent (Bob, Helen): has. Child
Typology of DLs l Constructors of Description logics AL l l Negation: A (A primitive) Conjunction: (A ⊓ B) Universal quantification: R. C Limited existential quantification: R. ⊤
Typology of DLs l Constructors of Description logics ALU l l Constructors of Description logics ALE l l R. C (full existencial quantification) Constructors of Description logics ALN l l (A ⊔ B) (disjunction) ( n C) , ( n C) (numerical restriction) Constructors of Description logics ALC l ( A) (full negation)
Typology of DLs l Description logics S l l ALCR+ = ALC + transitive roles axioms. Trans(has. Offspring) Description logics SH l SH = S + role hiearchy axioms. l has. Son has. Child Description logics SHf l l SHf = SH + role functional axioms. Func(R)
Typology of DLs l l Description logics SHO l SHO = SH + nominal axioms. l C {a} Description logics SHOI l l SHO = SH + inverse role axioms. Description logics SHOIN l SHOIN = SHOI + numerical restrictions.
Typology of DLs l Description logics SHOIQ l l SHOIQ = SHOI + qualified numerical restrictions. Description logics SROIQ l SROIQ = SHOIQ + extended role axioms l disjoint roles, reflexive and irreflexive roles, negated role assertions (A box), complex role inclusion axioms, local reflexivity axioms.
Important DLs l ALC – base DL SHOIN – OWL DL SROIQ – OWL DL 1. 1 l (Support for datatypes) l l
Uncertainty and Applications l Several Applications from Industry and Academic face uncertain imprecision: l l l Multimedia Processing (Image Analysis and Annotation) Medical Diagnosis Geospatial Applications Information Retrieval Sensor Readings Decision Making
Uncertainty l l l Imprecision (Possibility Theory) Vagueness (Fuzzy Set Theory) Randomness (Probability Theory)
Fuzzy Set Theory l An object belongs to a set to a degree between 0 and 1. (membership degree). l l Tall(George)=0. 7 A pair of objects belongs to a relation to a degree between 0 and 1. (membership degree). l Far(Prague, Paris)=0. 6
Fuzzy Set Theoretic Operations l Complement: c(x) l l Intersection: t(x, y) l l l t(x, y)=min(x, y), t(x, y)=max(0, x+y-1) t-norm Godel, Lukasiewicz Union: u(x, y) l l l c(x)=1 -x u(x, y)=max(x, y), u(x, y)=min(1, x+y) s-norm Godel, Lukasiewicz Implication: J(x, y) l l J(x, y)=max(1 -x, y), J(x, y)=min(1, 1 -x+y) Kleene-Dienes, Lukasiewicz
Fuzzy DLs l Syntax Extensions l l A box Fuzzy assertions: DLAssertion { , , >, <} [0, 1] l l George: Tall 0. 7, (Prague, Paris): Far 0. 6
Complex concepts l Bob: Tall 0. 8 Bob: Athletic 0. 6 l Bob: (Athletic ⊓ Tall) t(0. 6, 0. 8) l
Reasoning l l l Usually DL Reasoning is done with tableaux algorithms. Tableaux algorithms can be extended to deal with fuzziness NTU Athens - Implementation for f. KD-SHIN l Reasoner FIRE
Future l l Fuzzy T box l <C D> 0, 6 Fuzzy R box l <R S> 0, 3
Fuzzy SWRL
SWRL l A Semantic Web Rule Language Combining OWL and Rule. ML l l (undecidable) Rule. ML – Rule Markup Language l (www. ruleml. org)
Fuzzy SWRL l OWL – A box: l l 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). Rule. ML l atoms can include a “weight” (a truth value between 0 and 1) that represents the “importance” of the atom in a rule.
Fuzzy SWRL l Fuzzy rule assertions: l l l antecedent → consequent parent(? x, ? p) ∧ Happy(? p) → Happy(? x) *0. 8, Eyebrows. Raised(? a)*0. 9 ∧ Mouth. Open(? a)*0. 8 → Happy(? a)
Fuzzy Carin
Fuzzy Carin l Carin combines the description logic ALCNR with Horn Rules. l Fuzzy Carin adds fuzziness to Carin. l (decidable)
Fuzzy Carin
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