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Model Theory – Definite Semantics

  • The definite semantics again require a set of conditions to hold
  • We can now refer to every formula in E since they are guaranteed to have a truth value in the minimal model

 

  • Consistency:
      Prior Satisfiability: all e in E - are false in M +( B )
    • Negative evidence should not be part of the minimal model
      Posterior Satisfiability: all e in E - are false in M +( B H )
    • Negative evidence should not be supported by our hypotheses
  • Completeness
      Prior Necessity: some e in E + are false in M +( B )
    • If all positive examples are already true in the minimal model of the background knowledge, then no hypothesis we derive will add useful information
      Posterior Sufficiency: all e in E + are true in M +( B H )
    • All positive examples are true (explained by the hypothesis) in the minimal model of the background theory and the hypothesis

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