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Model Theory – Non-monotonic Semantics (2)

  • Since only positive evidence is present, it is assumed to be part of the background theory:
            B’ = B ∪ E
  • The following conditions should hold for H and B’:
    • Validity: all h in H are true in M +( B’ )
      • All clauses belonging to a hypothesis hold in the database B, i.e. that they are true properties of the data
    • Completeness: if general clause g is true in M +( B’ ) then H g
      • All information that is valid in the minimal model of B’ should follow from the hypothesis
  • Additionally the following can be a requirement:
    • Minimality: there is no proper subset G of H which is valid and complete
      • The hypothesis should not contain redundant clauses

Speaker notes:

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