Testclasses and closed world assumptions for non-horn theories

  • Jürgen Gehne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 619)


Given a sublattice ∑ of 1st-order sentences, the notions of the ∑-closed world assumption, the generalized ∑-closed world assumption and ∑-irreducibility of an arbitrary theory are investigated. It is shown that for a theory T there exists a finite number of ∑ irreducible extensions whose intersection equals T iff there exists a finite ∑-testclass for T, i.e. a finite set of models of T such that any sentence σ ∈ ∑ follows from T iff σ holds in all of these models. In this case, an axiomatizability result for the irreducible components is proved.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Jürgen Gehne
    • 1
  1. 1.Humboldt-Universität zu Berlin Fachbereich MathematikBerlinFRG

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