Knowledge Representation for the Semantic Web Lecture 4: Description - PowerPoint PPT Presentation

Modeling Description Logics and OWL Knowledge Representation for the Semantic Web Lecture 4: Description Logics III Daria Stepanova slides based on Reasoning Web 2011 tutorial “ Foundations of Description Logics and OWL ” by S. Rudolph Max Planck Institute for Informatics D5: Databases and Information Systems group WS 2017/18 1 / 33

Modeling Description Logics and OWL Unit Outline Modeling Description Logics and OWL 2 / 33

Modeling Description Logics and OWL Modeling 3 / 33

❼ ❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: 4 / 33

❼ ❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: Actor ( angelina ) 4 / 33

❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: Actor ( angelina ) ❼ individuals angelina and brad are in the relation of being married: 4 / 33

❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: Actor ( angelina ) ❼ individuals angelina and brad are in the relation of being married: married ( angelina , brad ) 4 / 33

❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: Actor ( angelina ) ❼ individuals angelina and brad are in the relation of being married: married ( angelina , brad ) ❼ every actor is an artist: 4 / 33

❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: Actor ( angelina ) ❼ individuals angelina and brad are in the relation of being married: married ( angelina , brad ) ❼ every actor is an artist: Actor ⊑ Artist ∀ x. Actor ( x ) → Artist ( x ) 4 / 33

Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: Actor ( angelina ) ❼ individuals angelina and brad are in the relation of being married: married ( angelina , brad ) ❼ every actor is an artist: Actor ⊑ Artist ∀ x. Actor ( x ) → Artist ( x ) ❼ every actor who is a US governor is also a bodybuilder or not Austrian: 4 / 33

Modeling Description Logics and OWL Modeling with DLs: Motivating Examples ❼ individual angelina belongs to the set of all actors: Actor ( angelina ) ❼ individuals angelina and brad are in the relation of being married: married ( angelina , brad ) ❼ every actor is an artist: Actor ⊑ Artist ∀ x. Actor ( x ) → Artist ( x ) ❼ every actor who is a US governor is also a bodybuilder or not Austrian: Actor ⊓ USGovernor ⊑ Bodybuilder ⊔ ¬ Austrian ∀ x. ( Actor ( x ) ∧ USGovernor ( x )) → ( BodyBuilder ( x ) ∨ ¬ Austrian ( x )) 4 / 33

❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ everybody knowing some actor has only envious friends: 5 / 33

❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ everybody knowing some actor has only envious friends: ∃ knows . Actor ⊑ ∀ hasfriend . Envious ∀ x ( ∃ y ( knows ( x, y ) ∧ Actor ( y )) → ∀ z ( hasfriend ( x, z ) → Envious ( z ))) 5 / 33

❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ everybody knowing some actor has only envious friends: ∃ knows . Actor ⊑ ∀ hasfriend . Envious ∀ x ( ∃ y ( knows ( x, y ) ∧ Actor ( y )) → ∀ z ( hasfriend ( x, z ) → Envious ( z ))) ❼ everybody having a child is the child of only grandparents: 5 / 33

❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ everybody knowing some actor has only envious friends: ∃ knows . Actor ⊑ ∀ hasfriend . Envious ∀ x ( ∃ y ( knows ( x, y ) ∧ Actor ( y )) → ∀ z ( hasfriend ( x, z ) → Envious ( z ))) ❼ everybody having a child is the child of only grandparents: ∃ hasChild . ⊤ ⊑ ∀ hasChild − . Grandparent ∀ x ( ∃ y ( hasChild ( x, y )) → ∀ z ( hasChild ( z, x ) → Grandparent ( x ))) 5 / 33

Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ everybody knowing some actor has only envious friends: ∃ knows . Actor ⊑ ∀ hasfriend . Envious ∀ x ( ∃ y ( knows ( x, y ) ∧ Actor ( y )) → ∀ z ( hasfriend ( x, z ) → Envious ( z ))) ❼ everybody having a child is the child of only grandparents: ∃ hasChild . ⊤ ⊑ ∀ hasChild − . Grandparent ∀ x ( ∃ y ( hasChild ( x, y )) → ∀ z ( hasChild ( z, x ) → Grandparent ( x ))) ❼ a polygamist is married to at least two distinct individuals: 5 / 33

Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ everybody knowing some actor has only envious friends: ∃ knows . Actor ⊑ ∀ hasfriend . Envious ∀ x ( ∃ y ( knows ( x, y ) ∧ Actor ( y )) → ∀ z ( hasfriend ( x, z ) → Envious ( z ))) ❼ everybody having a child is the child of only grandparents: ∃ hasChild . ⊤ ⊑ ∀ hasChild − . Grandparent ∀ x ( ∃ y ( hasChild ( x, y )) → ∀ z ( hasChild ( z, x ) → Grandparent ( x ))) ❼ a polygamist is married to at least two distinct individuals: Polygamist ⊑ ≥ 2 marriedTo . ⊤ ∀ x ( Polygamist ( x ) → ∃ y ∃ z ( marriedTo ( x, y ) ∧ marriedTo ( x, z ) ∧ y � = z )) 5 / 33

❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ being married to Brad is a property only applying to Angelina: 6 / 33

❼ ❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ being married to Brad is a property only applying to Angelina: ∃ marriedTo . { brad } ⊑ { angelina } ∃ x ( marriedTo ( x, brad ) → x = angelina ) 6 / 33

❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ being married to Brad is a property only applying to Angelina: ∃ marriedTo . { brad } ⊑ { angelina } ∃ x ( marriedTo ( x, brad ) → x = angelina ) ❼ being married to somebody implies loving them: 6 / 33

❼ Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ being married to Brad is a property only applying to Angelina: ∃ marriedTo . { brad } ⊑ { angelina } ∃ x ( marriedTo ( x, brad ) → x = angelina ) ❼ being married to somebody implies loving them: marriedTo ⊑ loves ∀ x ∀ y married ( x, y ) → loves ( x, y ) 6 / 33

Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ being married to Brad is a property only applying to Angelina: ∃ marriedTo . { brad } ⊑ { angelina } ∃ x ( marriedTo ( x, brad ) → x = angelina ) ❼ being married to somebody implies loving them: marriedTo ⊑ loves ∀ x ∀ y married ( x, y ) → loves ( x, y ) ❼ the child of somebody I am a child of is my sibling: 6 / 33

Modeling Description Logics and OWL Modeling with DLs: Motivating Examples, cont’d. ❼ being married to Brad is a property only applying to Angelina: ∃ marriedTo . { brad } ⊑ { angelina } ∃ x ( marriedTo ( x, brad ) → x = angelina ) ❼ being married to somebody implies loving them: marriedTo ⊑ loves ∀ x ∀ y married ( x, y ) → loves ( x, y ) ❼ the child of somebody I am a child of is my sibling: hasChild − ◦ hasChild ⊑ hasSibling ∀ x ∀ y ∀ z ( hasChild ( y, x ) ∧ hasChild ( y, z ) → hasSibling ( x, z )) 6 / 33

Modeling Description Logics and OWL Frequent Modeling Features ❼ domain ∃ authorOf . ⊤ ⊑ Person ❼ range ⊤ ⊑ ∀ authorOf . Publication ∃ authorOf − . ⊤ ⊑ Publication or ❼ concept disjointness Male ⊓ Female ⊑ ⊥ or Male ⊑ ¬ Female marriedWith ⊑ marriedWith − ❼ role symmetry ❼ role transitivity partOf ◦ partOf ⊑ partOf 7 / 33

Modeling Description Logics and OWL Number Restrictions ❼ allow for defining that a role is functional ⊤ ⊑ ≤ 1 hasFather . ⊤ ❼ ...or inverse functional ⊤ ⊑ ≤ 1 hasFather − . ⊤ ❼ allow for enforcing an infinite domain ( ∀ succ − . ⊥ )( zero ) ⊤ ⊑ ≤ 1 . succ − . ⊤ ⊤ ⊑ ∃ succ . ⊤ ❼ Consequently, DLs with number restrictions and inverses do not have the finite model property . 8 / 33

Modeling Description Logics and OWL Nominal Concept and Universal Role ❼ allow to restrict the size of concepts AtMostTwo ⊑ { one , two } AtMostTwo ⊑ ≤ 2 u. ⊤ ❼ even allow to restrict the size of the domain ⊤ ⊑ { one , two } ⊤ ⊑ ≤ 2 u. ⊤ 9 / 33

Modeling Description Logics and OWL Self-Restriction ❼ allows to define a role as reflexive ⊤ ⊑ ∃ knows . Self ❼ allows to define a role as irreflexive ∃ betterThan . Self ⊑ ⊥ ❼ together with number restrictions, we can even axiomatize equality ⊤ ⊑ ∃ equals . Self ⊤ ⊑ ≤ 1 equals . ⊤ 10 / 33