Negation as failure

The aim of this paper is a modification of Minker's Generalized Closed World Assumption that would allow application of the “negation as failure rule” with respect to a set P of (not necessarily all) predicates of a database DB. A careful closure procedure is introduced which, when applied to a database DB, produces a new database DB∗, that is used to answer queries about predicates from DB. It is shown that DB∗ is consistent iff DB is consistent. If P is the set of all predicates from DB and DB does not contain functional symbols, then DB∗ coincides with Minker's GCWA. The soundness and completeness of the careful closure procedure with respect to a minimal model style semantic is shown. As an inference engine associated with DB∗ we propose a query evaluation procedure QEP∗ which is a combination of a method of splitting an indefinite database DB into a disjunction of Horn databases and Clark's query evaluation procedure QEP. Soundness of QEP∗ with respect to DB∗ is shown for a broad class of databases.

Authors

• Michael Gelfond Ricardo A. Morales
• Halina Przymusinska

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