Classical Definitions Are Not Enough
Definitions provide equivalent expressions
(<=> (R ?x1 … ?xn) ??x1,…,?xn)
E.g., (<=> (bachelor ?x) (and (man ?x) (not (married ?x))))
Defined symbols can be eliminated by replacement
- Defined symbols are “non-primitive” symbols
KB is then expressed in terms of undefined symbols
- Undefined symbols are “primitive” symbols
Undefined symbols are given “meaning” by axioms
E.g., (not (and (on ?x ?y) (on ?y ?x)))
Thus, ontologies must have both definitions and axioms