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ece 720 intelligent web: ontology and beyond. lecture 15: description logic - introduction. description logic network-based representation structure. representing knowledge in a network form: nodes –used to characterize concepts (sets or classes of individual objects) - PowerPoint PPT Presentation
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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
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description logicnetwork-based representation structure
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Mother
Female
Person
Woman
Parent
hasChild(1, NIL)
v/r
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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
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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
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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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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)
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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) )
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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
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description logicnetwork-based structure – logical aspect
Person FemaleFemale Male
we talk about concept conjunction, … disjunction, negation
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description logicnetwork-based structure – logical aspect
key feature of DL – constructs for establishing relationships between conceptsthe basic ones are value restrictions + existential quantifications
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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)
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description logicnetwork-based structure – logical aspect
hasChild.Female-> individuals all of whose children are female
hasChild.Female-> individuals having a female baby
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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)
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description logicnetwork-based structure – logical aspect
value restrictions + existential quantifications are meant to characterize relationships between concepts
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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
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description logicnetwork-based structure – logical aspect
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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description logicreasoning
another typical inference on concepts is satisfiability
checking weather a concept expression does not necessarily denote the empty concept
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description logicreasoning
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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description logicknowledge representation
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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description logicknowledge representation
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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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
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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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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
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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
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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
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