Incomplete Information in Relational Databases
Journal of the ACM (JACM)
Finitely Specifiable Implicational Dependency Families
Journal of the ACM (JACM)
On the expressive power of data dependencies
Acta Informatica
Specification and implementation of programs for updating incomplete information databases
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Why Horn formulas matter in computer science: initial structures and generic examples
Journal of Computer and System Sciences
Independent and separable database schemes
SIAM Journal on Computing
Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Pairwise-definable subdirect decompositions of general database schemata
MFDBS 91 Proceedings of the 3rd symposium on Mathematical fundamentals of database and knowledge base systems
Foundations of canonical update support for closed database views
ICDT '90 Proceedings of the third international conference on database theory on Database theory
Decomposition of relational schemata into components defined by both projection and restriction
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A normal form for relational databases that is based on domains and keys
ACM Transactions on Database Systems (TODS)
Update semantics of relational views
ACM Transactions on Database Systems (TODS)
On interpretations of relational languages and solutions to the implied constraint problem
ACM Transactions on Database Systems (TODS)
A simplied universal relation assumption and its properties
ACM Transactions on Database Systems (TODS)
The theory of joins in relational databases
ACM Transactions on Database Systems (TODS)
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
Logic and Databases: A Deductive Approach
ACM Computing Surveys (CSUR)
Logic and Data Bases
Canonical view update support through boolean algebras of components
PODS '84 Proceedings of the 3rd ACM SIGACT-SIGMOD symposium on Principles of database systems
Algebraic aspects of relational database decomposition
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
What You Always Wanted to Know About Datalog (And Never Dared to Ask)
IEEE Transactions on Knowledge and Data Engineering
A sophisticate's introduction to database normalization theory
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
A normal form for abstract syntax
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
Independent components of databases
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
On the computation of relational view complements
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Uniqueness of Update Strategies for Database Views
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
On the computation of relational view complements
ACM Transactions on Database Systems (TODS)
An Order-Based Theory of Updates for Closed Database Views
Annals of Mathematics and Artificial Intelligence
The complexity of embedded axiomatization for a class of closed database views
Annals of Mathematics and Artificial Intelligence
Semantic Bijectivity and the Uniqueness of Constant-Complement Updates in the Relational Context
Semantics in Data and Knowledge Bases
Lossless decompositions in complex-valued databases
FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
Connecting keywords through pointer paths over the web
Proceedings of the 2005 international conference on Federation over the Web
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In earlier work, Bancilhon and Spyratos introduced the concept of a complement to a database schema, and showed how this notion could be used in theories of decomposition and update semantics. However, they also showed that, except in trivial cases, even minimal complements are never unique, so that many desirable results, such as canonical decompositions, cannot be realized. Their work dealt with database schemata which are sets and database mappings which are functions, without further structure. In this work, we show that by adding a modest amount of additional structure, many important uniqueness results may be obtained. Specifically, we work with database schemata whose legal states form partially ordered sets (posets) with least elements, and with database mappings which are isotonic and which preserve this least element. This is a natural algebraic structure which is inherent in many important examples, including relational schemata constrained by data dependencies, with views constructed by composition of projection, restriction, and selection. Other examples include deductive database schemata in which views are defined by rules, and general first-order logic databases. Within this context of posets, we show that direct (i.e., independent) complements must be unique, and that in fact the directly complementable views have the structure, in a very natural sense, of a Boolean algebra. Decompositions of the schema then become identifiable with finite subalgebras of this Boolean algebra. To demonstrate the utility of our approach, we examine in some detail its applicability to the relational model. Particularly, we establish that under the condition that the schema is constrained by universal Horn sentences, there is a unique ultimate decomposition into a finite set of type restrictions. The latter are a special class of views which includes classical projections which occur in direct decompositions. In particular, classical join-based decomposition is completely recovered within a framework which explicitly axiomatizes independence via null values.