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Completeness & Decidability (1)

  • Completeness : If a knowledge-base KB entails a statement S , we can prove S

  • Gödel Completeness Theorem : There exists a complete proof system for FOL

    • KB ⊨ Q ↔ KB ⊢ Q

    • Gödel proved that there exists a complete proof system for FOL.

    • Gödel did not come up with such a concrete proof system.

  • Robinson’s Completeness Theorem : Resolution is such a concrete complete proof system for FOL


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