1. ece 720 intelligent web: ontology and beyond
lecture 15: description logic
- introduction

2. description logic network-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
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3. description logic network-based representation structure
v/r
Person
hasChild
(1, NIL)
Female
Parent
Woman
Mother
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4. description logic network-based representation structure
in some cases more complex relationships are themselves represented as nodes in addition, concepts can have simple properties, often called attributes
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5. description logic network-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
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6. description logic network-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
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7. description logic network-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)
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8. description logic network-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) )
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9. description logic network-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
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10. description logic network-based structure – logical aspect
Person Female Female Male we talk about concept conjunction, … disjunction, negation
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11. description logic network-based structure – logical aspect
key feature of DL – constructs for establishing relationships between concepts the basic ones are value restrictions + existential quantifications
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12. description logic network-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)
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13. description logic network-based structure – logical aspect
hasChild.Female -> individuals all of whose children are female -> individuals having a female baby
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14. description logic network-based structure – logical aspect
hasChild.Female the second argument – Female – is called a filler of the role hasChild y hasChild(x,y) Female(y)
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15. description logic network-based structure – logical aspect
value restrictions + existential quantifications are meant to characterize relationships between concepts
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16. description logic network-based structure – logical aspect
numerical restrictions ( 3 hasChild) ( 2hasFemaleRelative) an individual who has at least three children and at most two female relatives
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17. description logic network-based structure – logical aspect
intersection of roles Woman 2( hasChild hasFemaleRelative) a woman having at most 2 daughters
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18. description logic reasoning
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)
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19. description logic reasoning
another typical inference on concepts is satisfiability checking weather a concept expression does not necessarily denote the empty concept
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20. description logic reasoning
computational complexity of reasoning versus the expressiveness of the language
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21. description logic knowledge 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
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22. description logic knowledge 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
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23. description logic knowledge 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
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24. description logic knowledge 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
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25. description logic TBox
contains concept definitions, the definition of a new concept in terms of other previously defined concepts Woman Person Female
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26. description logic TBox
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
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27. description logic TBox
the basic deduction service: logical implication, i.e., verifying weather a generic relationship (subsumpiton) is a logic consequence of the declarations in the TBox
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28. description logic ABox
contains extensional knowledge about the domain of interest – assertions about individuals, called membership assertions Female Person(ANNA) hasChild(ANNA, BILL)
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29. description logic ABox
the basic reasoning task: instance checking, i.e., checking weather a given individual is an instance (belongs to) a specified concept
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