ece 720 intelligent web ontology and beyond lecture
ece 720 intelligent web: ontology and beyond lecture 15: description logic - introduction of 29
description logic network-based representation structure representing knowledge in a network form: nodes – links – ece 720, winter ‘ 12 used to characterize concepts (sets or classes of individual objects) used to characterize relationships among them 2 of 29
description logic network-based representation structure Person v/r has. Child (1, NIL) Female Parent Woman Mother ece 720, winter ‘ 12 3 of 29
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 ece 720, winter ‘ 12 4 of 29
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 ece 720, winter ‘ 12 5 of 29
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 ece 720, winter ‘ 12 6 of 29
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) ece 720, winter ‘ 12 7 of 29
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) ) ece 720, winter ‘ 12 8 of 29
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 ece 720, winter ‘ 12 9 of 29
description logic network-based structure – logical aspect Person Female Male we talk about concept conjunction, … disjunction, negation ece 720, winter ‘ 12 10 of 29
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 ece 720, winter ‘ 12 11 of 29
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) ece 720, winter ‘ 12 12 of 29
description logic network-based structure – logical aspect has. Child. Female -> individuals all of whose children are female has. Child. Female -> individuals having a female baby ece 720, winter ‘ 12 13 of 29
description logic network-based structure – logical aspect has. Child. Female the second argument – Female – is called a filler of the role has. Child y has. Child(x, y) ece 720, winter ‘ 12 Female(y) 14 of 29
description logic network-based structure – logical aspect value restrictions + existential quantifications are meant to characterize relationships between concepts ece 720, winter ‘ 12 15 of 29
description logic network-based structure – logical aspect numerical restrictions ( 3 has. Child) ( 2 has. Female. Relative) an individual who has at least three children and at most two female relatives ece 720, winter ‘ 12 16 of 29
description logic network-based structure – logical aspect intersection of roles Woman 2( has. Child has. Female. Relative) a woman having at most 2 daughters ece 720, winter ‘ 12 17 of 29
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) ece 720, winter ‘ 12 18 of 29
description logic reasoning another typical inference on concepts is satisfiability checking weather a concept expression does not necessarily denote the empty concept ece 720, winter ‘ 12 19 of 29
description logic reasoning computational complexity of reasoning versus the expressiveness of the language ece 720, winter ‘ 12 20 of 29
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 ece 720, winter ‘ 12 21 of 29
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 ece 720, winter ‘ 12 22 of 29
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 ece 720, winter ‘ 12 23 of 29
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 ece 720, winter ‘ 12 24 of 29
description logic TBox contains concept definitions, the definition of a new concept in terms of other previously defined concepts Woman ece 720, winter ‘ 12 Person Female 25 of 29
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 ece 720, winter ‘ 12 26 of 29
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 ece 720, winter ‘ 12 27 of 29
description logic ABox contains extensional knowledge about the domain of interest – assertions about individuals, called membership assertions Female Person(ANNA) has. Child(ANNA, BILL) ece 720, winter ‘ 12 28 of 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 ece 720, winter ‘ 12 29 of 29
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