Classical Definitions Are Not Enough

• Definitions provide equivalent expressions

  R(x) ? ?(x)
  
  E.g., bachelor(x) ? man(x) ? ~married(x)

• Defined symbols can be eliminated by replacement

• KB is then expressed in terms of undefined symbols

• Undefined symbols are given “meaning” by axioms

  E.g., ~[on(x,y) ? on(y,x)]
  

• Thus, ontologies must have both definitions and axioms

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