Part II: OWL - Foundations of Semantic Web Technologies

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OWL Direct Semantics mapping is extended to complex class expressions: > I = ∆ I ⊥ I = ∅ (C u D) I = C I ∩ D I (C t D) I = C I ∪ D I (¬C) I = ∆ I \C I ∀R.C = { x | ∀(x,y) ∈ R I → y ∈ C I } ∃R.C = { x | ∃(x,y) ∈ R I ∧ y ∈ C I } ≥nR.C = { x | #{ y | (x,y) ∈ R I ∧ y ∈ C I } ≥ n} ≤nR.C = { x | #{ y | (x,y) ∈ R I ∧ y ∈ C I } ≤ n} ...and to role expressions: U I = ∆ I ×∆ I (R – ) I = { (y,x) | (x,y) ∈ R I } ...and to axioms: C(a) holds, if a I ∈ C I C v D holds, if C I ⊆ D I Dis(R,S) holds if R I ∩ S I = ∅ R(a,b) holds, if (a I ,b I ) ∈ R I R v S holds, if R I ⊆ S I S 1 oS 2 o ... oS n v R holds if S 1 I oS 2 I o ... oS n I ⊆ R I 40
OWL Direct Semantics via FOL but often OWL 2 DL is said to be a fragment of FOL (with equality)... yes, there is a translation of OWL 2 DL into FOL ...which (interpreted under FOL semantics) coincides with the definition just given. 41
Page 1 and 2: Semantic Web Modelling Languages (P
Page 3 and 4: OWL - Overview Web Ontology Languag
Page 5 and 6: References - Textbooks Pascal Hitzl
Page 7 and 8: Contents OWL - Basic Ideas OWL As t
Page 9 and 10: OWL Building Blocks individuals (wr
Page 11 and 12: DL syntax RDFS syntax Person(mary)
Page 13 and 14: Class constructors conjunction Moth
Page 17 and 18: Understanding SROIQ(D) ALC + role c
Page 19 and 20: Understanding SROIQ(D) I - inverse
Page 21 and 22: Understanding SROIQ(D) (D) - dataty
Page 23 and 24: Understanding SROIQ(D) further expr
Page 25 and 26: Some Syntactic Sugar in OWL This ap
Page 27 and 28: OWL - Extralogical Features OWL ont
Page 29 and 30: The RDFS perspective RDFS semantics
Page 33 and 34: Expressivity Examples: Rules in OWL
Page 35 and 36: OWL Semantics There are two semanti
Page 37 and 38: OWL Direct Semantics: Restrictions
Page 39: OWL Direct Semantics model-theoreti
Page 43 and 44: OWL Profiles OWL Full - using the R
Page 45 and 46: OWL 2 RL motivated by the question:
Page 47 and 48: OWL 2 QL motivated by the question:
Page 49 and 50: Proof Theory Traditionally using ta
Page 51 and 52: DL Tableaux Termination Problem TBo
Page 53 and 54: Blocking (in ALC) y is blocked (by
Page 55 and 56: ALC Tableau Example TBox: ¬C t ∀
Page 57 and 58: OWL tools (incomplete listing) Reas
Page 59 and 60: Some Current Research Questions Int
Page 61 and 62: Suggestions for OWL? Annual Worksho
Page 63 and 64: Main References W3C OWL Working Gro
Page 65 and 66: Further References DL complexity ca

Part II: OWL - Foundations of Semantic Web Technologies

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