Axiomatisation of functional dependencies in incomplete relations

Levene, Mark and Loizou, G. (1998) Axiomatisation of functional dependencies in incomplete relations. Theoretical Computer Science 206 (1-2), pp. 283-300. ISSN 0304-3975.

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Official URL: https://doi.org/10.1016/S0304-3975(98)80029-7

Abstract

Incomplete relations are relations which contain null values, whose meaning is “value is at present unknown”. Such relations give rise to two types of functional dependency (FD). The first type, called the strong FD (SFD), is satisfied in an incomplete relation if for all possible worlds of this relation the FD is satisfied in the standard way. The second type, called the weak FD (WFD), is satisfied in an incomplete relation if there exists a possible world of this relation in which the FD is satisfied in the standard way. We exhibit a sound and complete axiom system for both strong and weak FDs, which takes into account the interaction between SFDs and WFDs. An interesting feature of the combined axiom system is that it is not k-ary for any natural number k ⩾ 0. We show that the combined implication problem for SFDs and WFDs can be solved in time polynomial in the size of the input set of FDs. Finally, we show that Armstrong relations exist for SFDs and WFDs.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	08 Jun 2021 11:07
Last Modified:	09 Aug 2023 12:51
URI:	https://eprints.bbk.ac.uk/id/eprint/44640

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