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) links – used to characterize relationships among them ece 720, winter ‘12

description logic network-based representation structure v/r Person hasChild (1, NIL) Female Parent Woman Mother ece 720, winter ‘12

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

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

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

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

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

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

description logic network-based structure – logical aspect Person Female Female Male we talk about concept conjunction, … disjunction, negation ece 720, winter ‘12

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

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

description logic network-based structure – logical aspect hasChild.Female -> individuals all of whose children are female -> individuals having a female baby ece 720, winter ‘12

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) ece 720, winter ‘12

description logic network-based structure – logical aspect value restrictions + existential quantifications are meant to characterize relationships between concepts ece 720, winter ‘12

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 ece 720, winter ‘12

description logic network-based structure – logical aspect intersection of roles Woman 2( hasChild hasFemaleRelative) a woman having at most 2 daughters ece 720, winter ‘12

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

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

description logic reasoning computational complexity of reasoning versus the expressiveness of the language ece 720, winter ‘12

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

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

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

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

description logic TBox contains concept definitions, the definition of a new concept in terms of other previously defined concepts Woman Person Female ece 720, winter ‘12

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

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

description logic ABox contains extensional knowledge about the domain of interest – assertions about individuals, called membership assertions Female Person(ANNA) hasChild(ANNA, BILL) ece 720, winter ‘12

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