Foundations of a functional approach to knowledge representation.
Artificial Intelligence
Incomplete Information in Relational Databases
Journal of the ACM (JACM)
A sound and sometimes complete query evaluation algorithm for relational databases with null values
Journal of the ACM (JACM)
Journal of Computer and System Sciences
An algebraic evaluation method for deduction in incomplete data bases
Journal of Logic Programming
The relational model for database management: version 2
The relational model for database management: version 2
A family of incomplete relational database models
VLDB '89 Proceedings of the 15th international conference on Very large data bases
On semantic issues connected with incomplete information databases
ACM Transactions on Database Systems (TODS)
Extending the database relational model to capture more meaning
ACM Transactions on Database Systems (TODS)
On Databases with Incomplete Information
Journal of the ACM (JACM)
Null values in data base management a denotational semantics approach
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
TARK '88 Proceedings of the 2nd conference on Theoretical aspects of reasoning about knowledge
Multivalued dependencies with null values in relational data bases
VLDB '79 Proceedings of the fifth international conference on Very Large Data Bases - Volume 5
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The introduction of nulls (unknown values) in the relational database calls for an extension of the theoretical foundation of the database model. Nulls are alien to classical logic, in which the relational database model is rooted. This has led to all sorts of counterintuitive ad hoc solutions, reasonable in one place, but awkward in others. A sound model-theoretical foundation of nulls in a relational database based on modal logic is presented here. The modal interpretation of queries is easy to comprehend and intuitively correct. Partial interpretations, which are to be preferred from a computational point of view, are inadequate for arbitrary queries. Formulas that have an identical partial and modal interpretation are called safe. Safety guarantees on the one hand that the partial answer is meaningful and on the other hand that the modal interpretation is finitely computable. The suitability of modal logic to model nulls is illustrated by a short discussion of the effect of nulls on database integrity.