### Equality and Domain Closure in First-Order DatabasesEquality and Domain Closure in First-Order Databases

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 Author Reiter, Raymond Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1980 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract A class of first-order databases with no function signs is considered. A closed database DB is one for which the only existing individuals are those explicitly referred to in the formulas of DB. Formally, this is expressed by including in DB a domain closure axiom $(\textit{x})\textit{x}$ = $\textit{c}1$ ∨···∨ $\textit{x}$ = $\textit{cp},$ where $\textit{c}1,…,\textit{cp}$ are all of the constants occurring in DB. It is shown how to completely capture the effects of this axiom by means of suitable generalizations of the projection and division operators of relational algebra, thereby permitting the underlying theorem prover used for query evaluation to ignore this axiom.A database is E-saturated if all of its constants denote distinct individuals. It is shown that such databases circumvent the usual problems associated with equality, which arise in more general databases.Finally, it is proved for Horn databases and positive queries that only definite answers are obtained, and for databases with infinitely many constants that infinitely long indefinite answers can arise. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1980-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 27 Issue Number 2 Page Count 15 Starting Page 235 Ending Page 249

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Source: ACM Digital Library