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# Description logics

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### Description logics

1. 1. Description Logic Rajendra Akerkar jWestern Norway Research Institute, Norway
2. 2. Knowledge Representation f facilitate inferencing f g Inferencing often involves making classes o of objects, defining a hierarchy, giving e g e a c y, g v g attributes to objects and specifying constraints. R. Akerkar 2
3. 3. Predicate Calculus Uses (i) Predicates for describing relationships and (ii) Rules for inferencing A special kind of inferencing is Inheritance where all properties of a super class are passed onto its subclasses For F example, it can b inferred that men- b i l i be i f d h being human have 2 legs by virtue of their inheriting human-properties. human-properties R. Akerkar 3
4. 4. Structured Knowledge Representation Components and their interrelationships have to be expressed Semantic Nets and Frames prove more effective than predicate calculus Reminiscent of calculus where using differentiation to find the rate of change of one q y p quantity with respect to another is more convenient than using the more foundational y Lt L x 0 x R. Akerkar 4
5. 5. Semantic Net R. Akerkar 5
6. 6. Frames(example f l from medical entities dictionary, Columbia di l i i di i C l biUniversity) Have slots and fillers R. Akerkar 6
7. 7. Motivation to study Structure of the knowledge may not be visible, and obvious inferences may be difficult to draw Expressive power is too high for obtaining decidable and efficient inference Inference power may be too low f I f b l for expressing interesting, but still decidable theories R. Akerkar 7
8. 8. Wikipedia Definition “Description logics (DL) are a family of knowledge representation languages which can be used to represent the terminological knowledge of an application domain in a structured and formally well- understood way. The name description logic refers on the way refers, one hand, to concept descriptions used to describe a domain and, on the other hand, to the logic-based semantics which can be given by a translati n int first hich i en b translation into first- order predicate logic. Description logic was designed as an extension to frames and semantic networks, which were not equipped with formal logic-based semantics.” t i d ith f ll i b d ti ” R. Akerkar 8
9. 9. Constituents of DL Individuals (such as Ralf and John) ( f J ) Concepts (such as Man and Woman) Roles (such as isStudent)Individuals are like constants in predicate calculus,while Concepts are like Unary predicatesand Roles are like Binary Predicates. R. Akerkar 9
10. 10. Constructors of DL and theirmeaningConstructor Syntax Example Semantics using PCAtomic Concept A Human {x | human(x)}Atomic Role R Has-child { y {<x,y> | has-child(x,y)} ( y)}Conjunction C∩D Human ∩ Male {x | human(x)  male(x)}Disjunction CD Doctor  Lawyer {x | doctor(x)  lawyer(x)}Negation C Male {x | male(x)}Exists Restriction  R.C  Has-child.Male {x |  y has-child(x,y)  male(y)}Value Restriction  R.C Has-child.Doctor {x | y has-child(x,y) doctor(y)} R. Akerkar 10
11. 11. Examples For example the set of all those p p parents having a male child who is a doctor or a lawyer is expressed as y p Has-child.Male ∩( Doctor U Lawyer) R. Akerkar 11
12. 12. Quantifiers and ‘Dots’ Dots HasChild.Girl is interpreted as the set ◦ {x | (y)( HasChild(x,y)Girl(y))} and isEmployedBy.Farmer is interpreted as p y y p ◦ {x | (y)( isEmployedBy(x,y) Farmer(y))} R. Akerkar 12
13. 13. Inference in DL Main mechanism: Inheritance via subsumption DL suitable for ontology engineering A concept C subsumes a concept D iff I(D)  I(C) on every interpretation I For example: Person subsumes Male, Parent subsumes Father etc Every attribute of a etc. concept is also present in the subsumed concepts R. Akerkar 13