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Proof Theory of ILP

  • Inductive inference rules can be obtained by inverting deductive ones
    • Deduction: Given B ⋀ H ⊧ E + , derive E + from B ⋀ H
    • Induction: Given B ⋀ H ⊧ E + , derive H from B and B and E +
  • Inverting deduction paradigm can be studied under various assumptions, corresponding to different assumptions about the deductive rule for ⊧ and the format of background theory B and evidence E +
    ⇒ Different models of inductive inference are obtained
  • Example: θ -subsumption
    • The background knowledge is supposed to be empty, and the deductive inference rule corresponds to θ-subsumption among single clauses

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