On the relationship between circumscription and negation as failure

✍ Scribed by Michael Gelfond; Halina Przymusinska; Teodor Przymusinski

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 940 KB
• Volume: 38
• Category: Article
• ISSN: 0004-3702
• DOI: 10.1016/0004-3702(89)90068-4

✦ Synopsis

The aim of this paper is to investigate two powerful methods of handling negative information in logic-based knowledge representation systems: the logical minimization in the form of circumscription and the negation as failure rule, formalized by various closures (or completions) of original theories. We suggest a new, more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription. These results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories. This allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories.