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Model Theory – Normal Semantics

  • The problem of inductive inference:
    • Given is background (prior) knowledge B and evidence E
    • The evidence E = E+ ∪ E- consists of positive evidence E+ and negative evidence E-
    • The aim is then to find a hypothesis H such that the following conditions hold:
        Prior Satisfiability: B ∪ E- ⊭ □
        Posterior Satisfiability: B ∪ H ∪ E- ⊭ □
        Prior Necessity: B ⊭ E+
        Posterior Sufficiency: B ∪ H ⊧ E+
  • The Sufficiency criterion is sometimes named completeness with regard to positive evidence
  • The Posterior Satisfiability criterion is also known as consistency with the negative evidence
  • In this general setting, background-theory, examples, and hypotheses can be any (well-formed) formula

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