ece 720 intelligent web: ontology and beyond

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lecture 15: description logic - introduction

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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

ece 720, winter ‘12 2

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Mother

Female

Person

Woman

Parent

hasChild(1, NIL)

v/r

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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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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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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


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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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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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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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Person FemaleFemale Male

we talk about concept conjunction, … disjunction, negation


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key feature of DL – constructs for establishing relationships between conceptsthe basic ones are value restrictions + existential quantifications


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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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hasChild.Female-> individuals all of whose children are female

hasChild.Female-> individuals having a female baby


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hasChild.Female

the second argument – Female – is called a filler of the role hasChild

y hasChild(x,y) Female(y)


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value restrictions + existential quantifications are meant to characterize relationships between concepts


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numerical restrictions

( 3 hasChild) ( 2hasFemaleRelative)

an individual who has at least three children and at most two female relatives


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intersection of roles

Woman 2( hasChild hasFemaleRelative)

a woman having at most 2 daughters


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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)


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another typical inference on concepts is satisfiability

checking weather a concept expression does not necessarily denote the empty concept


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computational complexity of reasoning versus

the expressiveness of the language


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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


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


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TBoxcontains intentional knowledge in a form of a terminology and built through declarations that describe general properties of conceptssubject to occasional change


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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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description logicTBox

contains concept definitions, the definition of a new concept in terms of other previously defined concepts

Woman Person Female


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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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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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description logicABox

contains extensional knowledge about the domain of interest – assertions about individuals, called membership assertions

Female Person(ANNA)

hasChild(ANNA, BILL)


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description logicABox

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


ece 720 intelligent web: ontology and beyond

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