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Logical Expressions for the Definition of Concepts

  • The definition of a concept is a logical expression which can be used to define formally the semantics of the concept
    • The logical expression defines (or restricts, respectively) the extension (i.e. the set of instances) of the concept. If C is the identifier denoting the concept then the logical expression takes one of the following forms 
      forAll ?x ( ?x memberOf C implies l-expr(?x) ) 
      forAll ?x ( ?x memberOf C impliedBy l-expr(?x) ) 
      forAll ?x ( ?x memberOf C equivalent l-expr(?x) ) 
      where l-expr(?x) is a logical expression with precisely one free variable ?x
  • Example: The concept “Human” is defined as the intersection of the concepts “Primate” and “LegalAgent”

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