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Limitations of First-OrderTheorem Proving

  • From a practical point of view this is problematic
    • We cannot distinguish between the non-existence of a proof or the failure of an implementation to simply find a proof in reasonable time.
    • Theoretical completeness of an inference procedure does not make a difference in this cases
      • Does a proof simply take too long or will the computation never halt anyway?

  • Due to its complexity and remaining limitations FOL is often not suitable for practical applications

  • Often less expressive (but decideable) formalisms or formalisms with different expressivity are more suitable:
    • Description Logics
    • Logic Programming

Speaker notes:

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