e ce 627 intelligent web: ontology and beyond

1. ece 627intelligent web: ontology and beyond lecture 15: description logic - introduction

2. description logicnetwork-based representation structure representing knowledge in a network form: nodes – used to characterize concepts (sets or classes of individual objects) links – used to characterize relationships among them

3. description logicnetwork-based representation structure v/r Person hasChild (1, NIL) Female Parent Woman Mother

4. description logicnetwork-based representation structure in some cases more complex relationships are themselves represented as nodes in addition, concepts can have simple properties, often called attributes

5. description logicnetwork-based representation structure the is-a relationship defines a hierarchy over the concepts and provides the basis for the “inheritance of properties” a characteristic feature of Description Logics (DLs) is their ability to represent other kinds of relationship that can hold between concepts

6. description logicnetwork-based structure – logical aspect a precise characterization of the meaning of a network can be given by defining a language of the elements of the structure and by providing an interpretation for the strings of that language

7. description logicnetwork-based structure – logical aspect so … two disjoint alphabets of symbols that are used to denote atomic concepts (unary predicate symbols), and atomic roles (binary predicate symbols)

8. description logicnetwork-based structure – logical aspect terms are built from basic symbols using several kinds of constructors, for example intersection of concepts: C D ( C(x) D(x) )

9. description logicnetwork-based structure – logical aspect concepts are given a set-theoretic interpretation: a concept is interpreted as a set of individuals, and roles are interpreted as sets of pairs of individuals the non-finiteness of the domain and the open-world assumption are distinguished features of DL

10. description logicnetwork-based structure – logical aspect Person Female Female Male we talk about concept conjunction, … disjunction, negation

11. description logicnetwork-based structure – logical aspect key feature of DL – constructs for establishing relationships between concepts the basic ones are value restrictions + existential quantifications

12. description logicnetwork-based structure – logical aspect R.C - requires that all individuals that are in the relationship R with the concept being described belong to the concept C (all individuals that are in the relationship R with an individual described by the concept in question are themselves describable as C’s)

13. description logicnetwork-based structure – logical aspect hasChild.Female -> individuals all of whose children are female hasChild.Female -> individuals having a female baby

14. description logicnetwork-based structure – logical aspect hasChild.Female the second argument – Female – is called a filler of the role hasChild y hasChild(x,y) Female(y)

15. description logicnetwork-based structure – logical aspect value restrictions + existential quantifications are meant to characterize relationships between concepts

16. description logicnetwork-based structure – logical aspect numerical restrictions ( 3 hasChild) ( 2hasFemaleRelative) an individual who has at least three children and at most two female relatives

17. description logicnetwork-based structure – logical aspect intersection of roles Woman 2( hasChildhasFemaleRelative) a woman having at most 2 daughters

18. description logicreasoning the basic inference on concepts is subsumption C D checking weather the concept denoted by D (the subsumer) is considered more general than the one denoted by C (the subsumee)

19. description logicreasoning another typical inference on concepts is satisfiability checking weather a concept expression does not necessarily denote the empty concept

20. description logicreasoning computational complexity of reasoning versus the expressiveness of the language

21. description logicknowledge representation two aspects: • a precise characterization of a knowledge base (type of knowledge to be specified and reasoning services – what kind of questions the system should be able to answer) • a rich development environment

22. description logicknowledge representation intentional knowledge … “defined” by explicitly specifying all the properties required to come to a definition extensional knowledge … “defined” by listing every object that falls under the definition of the concept or term in question

23. description logicknowledge representation TBox contains intentional knowledge in a form of a terminology and built through declarations that describe general properties of concepts subject to occasional change

24. description logicknowledge representation ABox contains extensional knowledge – also called assertional knowledge – knowledge that is specific to the individuals of the domain of discourse usually thought not to change

25. description logicTBox contains concept definitions, the definition of a new concept in terms of other previously defined concepts Woman Person Female

26. description logicTBox two important assumptions: • only one definition for a concept name is allowed • definitions are acyclic – concepts are neither defined in terms of themselves not in terms of other concepts that indirectly refer to them

27. description logicTBox the basic deduction service: logical implication, i.e., verifying weather a generic relationship (subsumpiton) is a logic consequence of the declarations in the TBox

28. description logicABox contains extensional knowledge about the domain of interest – assertions about individuals, called membership assertions Female Person(ANNA) hasChild(ANNA, BILL)

29. description logicABox the basic reasoning task: instance checking, i.e., checking weather a given individual is an instance (belongs to) a specified concept