Abstract
A database is said to be indefinite if there is an answer to a query of the form Pa V Pb where neither Pa nor Pb can be derived from the database. Indefinite databases arise where, in general, the data consists of non-Horn clauses. A clause is non-Horn if it is a disjunction of literals in which more than one literal in the clause is positive.
Horn databases, which comprise most databases in existence, do not admit answers of the form Pa V Pb where neither Pa nor Pb are derivable from the database. It has been shown by Reiter that in such databases one can make an assumption, termed the Closed World Assumption (CWA), that to prove that ¯Pa is true, one can try to prove Pa, and if the proof for Pa fails, one can assume ¯Pa is true.
When a database consists of Horn and non-Horn clauses, Reiter has shown that it is not possible to make the CWA. In this paper we investigate databases that consist of Horn and non-Horn clauses. We extend the definition of CWA to apply to such databases. The assumption needed for such databases is termed the Generalized Closed World Assumption (GCWA). Syntactic and semantic definitions of generalized closed worlds are given. It is shown that the two definitions are equivalent. In addition, given a class of null values it is shown that the GCWA gives a correct interpretation for null values.
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© 1982 Springer-Verlag Berlin Heidelberg
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Minker, J. (1982). On indefinite databases and the closed world assumption. In: Loveland, D.W. (eds) 6th Conference on Automated Deduction. CADE 1982. Lecture Notes in Computer Science, vol 138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000066
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DOI: https://doi.org/10.1007/BFb0000066
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