NDLI: Safety and translation of relational calculus

Content Provider	ACM Digital Library
Author	Topor, Rodney W. Van gelder, Allen
Copyright Year	1991
Abstract	Not all queries in relational calculus can be answered sensibly when disjunction, negation, and universal quantification are allowed. The class of relation calculus queries or formulas that have sensible answers is called the domain independent class which is known to be undecidable. Subsequent research has focused on identifying large decidable subclasses of domain independent formulas. In this paper we investigate the properties of two such classes: the $\textit{evaluable}$ formulas and the $\textit{allowed}$ formulas. Although both classes have been defined before, we give simplified definitions, present short proofs of their main properties, and describe a method to incorporate equality.Although evaluable queries have sensible answers, it is not straightforward to compute them efficiently or correctly. We introduce relational algebra normal form for formulas from which form the correct translation into relational algebra is trivial. We give algorithms to transform an evaluable formula into an equivalent $\textit{allowed}$ formula and from there into relational algebra normal form. Our algorithms avoid use of the so-called $\textit{Dom}$ relation, consisting of all constants appearing in the database or the query. Finally, we describe a restriction under which every domain independent formula is evaluable and argue that the class of evaluable formulas is the largest decidable subclass of the domain independent formulas that can be efficiently recognized.
Starting Page	235
Ending Page	278
Page Count	44
File Format	PDF
ISSN	03625915
e-ISSN	15574644
DOI	10.1145/114325.103712
Volume Number	16
Issue Number	2
Journal	ACM Transactions on Database Systems (TODS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1991-05-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Allowed formulas Domain independence Evaluable formulas Existential normal Query translation Relational algebra Relational calculus
Content Type	Text
Resource Type	Article
Subject	Information Systems

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