Abstract
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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© 1992 Springer-Verlag Berlin Heidelberg
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Gehne, J. (1992). Testclasses and closed world assumptions for non-horn theories. In: Pearce, D., Wansing, H. (eds) Nonclassical Logics and Information Processing. All-Berlin 1990. Lecture Notes in Computer Science, vol 619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031923
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DOI: https://doi.org/10.1007/BFb0031923
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