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Introduction – Basic example

  • Consistency:
    • First, we must check that our problem has a solution:
            B ∪ E- ⊭ □ ( prior satisfiability )
      • If one of the negative examples can be proved to be true from the background information alone, then any hypothesis we find will not be able to compensate for this. The problem is not satisfiable.
    • B and H are consistent with E-:
            B ∪ H ∪ E- ⊭ □ ( posterior satisfiability )
      • After adding a hypothesis it should still not be possible to prove a negative example.
  • Completeness:
    • However, H allows us to explain E+ relative to B:
            B ∪ H ⊧ E+ ( posterior sufficiency )
      • This means that H should fit the positive examples given.

Speaker notes:

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