The Semantic Web – WEEK 10: Introduction to Description Logics The “Layer Cake” Model – [From Rector & Horrocks Semantic Web cuurse] We are back down to here!

The Semantic Web Recap First order logic is an expressive precise well-researched representation language family, and has systematic semi- decidable proof procedures like resolution refutation for automated reasoning. BUT FOL has drawbacks – it is too perhaps too expressive and unstructured

The Semantic Web Description Logic is a FAMILY of languages which have been used to give a semantics to - OO modelling languages such as E-R diagrams and UML class diagrams - Diagrammatic representations such as ‘Semantic Nets’ - Ontology languages such as OWL DL relates to u formal methods in software engineering, u database u AI

The Semantic Web Description Logic is centred around CLASSES F O Logic allows the user to make assertions about sets of individuals.. Eg Ax (P(x) => …) Ex (P(x) & …) DL allows the user to NAME SETS OF INVIDUALS for which some property is true and COMBINE these with other. P = { x | P(x) }

The Semantic Web Description Logics from F.O.Logic Description Logic Domain Individual Concept (or Class) Role (or Property) no equivalent!! Restricted use F.O.Logic Universe Constant name One-place predicate Two-place predicate > 2 place predicate Variables Functions Connectives Quantifiers

The Semantic Web Description Logics from F.O.Logic: Concepts Description Logic A concept C  {x | wff} P  Q Q subsumes P P  ¬ Q Q and P are disjoint P  Q P is equivalent to Q C  P  Q C  P U Q F.O.Logic One place predicate C Ax P(x) => Q(x) Ax P(x) => ¬ Q(x) Ax P(x)  Q(x) Ax C(x)  P(x) & Q(x) Ax C(x)  P(x) V Q(x) Examples 1.Postgrads are (defined as) students who have a first degree 2.Professors are also Doctors

The Semantic Web Description Logics from F.O.Logic: Roles Description Logic A role R = {(x.y) | R(x,y) } R  S - inverse role S - = {(x,y) | R(y,x)} R  S R  S R is transitive F.O.Logic Two place predicate AxAy R(x,y)  S(y,x) AxAy R(x,y)  S(x,y) AxAy R(x,y) => S(x,y) AxAyAz R(x,y) & R(y,z) => R(x,z)

The Semantic Web Concept Expressions Wffs are expressions whose value is true or false In DL, concept expressions denote a set of individuals for which the value of a wffs is TRUE C = {x | C(x) } P  Q = {x | P(x) & Q(x)} P U Q = {x | P(x) V Q(x)} P U ¬Q = {x | P(x) V ¬Q(x)}

The Semantic Web Concept Expressions with Roles some values from: E R.P = {x | Ey R(x,y) & P(x)} General form “E Role.Class” Examples: E Father.Male = “the set of fathers who have sons” Student  E Married.Student = “the set of students who also are married to students”

The Semantic Web Concept Expressions with Roles All values from: A R.P = {x | Ay R(x,y) => P(y)} General form “A Role.Class” Examples: Parents  A Parentof.Doctor “the set of parents whose children are (all) doctors” Students  A Examinedby.Easy “the set of students who had easy exams“

The Semantic Web Summary DL is built around classes – It is a logic with no variables or functions, and a restricted number of expressions compared to FOL