caa a22 4500 463187172 CHVBK 20180406164857.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10472-007-9067-0 doi (NATIONALLICENCE)springer-10.1007/s10472-007-9067-0 Full hierarchical dependencies in fixed and undetermined universes [Elektronische Daten] [Sven Hartmann, Henning Köhler, Sebastian Link] Full hierarchical dependencies (FHDs) constitute a large class of relational dependencies. A relation exhibits an FHD precisely when it is the natural join over at least two of its projections that all share the same join attributes. Therefore, FHDs generalise multivalued dependencies (MVDs) in which case the number of these projections is precisely two. The implication of FHDs has originally been defined in the context of some fixed finite universe. This paper identifies a sound and complete set of inference rules for the implication of FHDs. This axiomatisation is very reminiscent of that for MVDs. Then, an alternative notion of FHD implication is introduced in which the underlying set of attributes is left undetermined. The first main result establishes a finite axiomatisation for FHD implication in undetermined universes. It is then formally clarified that the complementation rule is only a mere means for database normalisation. In fact, the second main result establishes a finite axiomatisation for FHD implication in fixed universes which allows to infer FHDs either without using the complementation rule at all or only in the very last step of the inference. This also characterises the expressiveness of an incomplete set of inference rules in fixed universes. The results extend previous work on MVDs byBiskup. Springer Science+Business Media B.V., 2007 Relational database nationallicence Full hierarchical dependency nationallicence Implication nationallicence Inference nationallicence Hartmann Sven Information Science Research Centre, Dept. of Information Systems, Massey University, Palmerston North, New Zealand aut Köhler Henning Information Science Research Centre, Dept. of Information Systems, Massey University, Palmerston North, New Zealand aut Link Sebastian Information Science Research Centre, Dept. of Information Systems, Massey University, Palmerston North, New Zealand aut Annals of Mathematics and Artificial Intelligence Springer Netherlands 50/1-2(2007-06-01), 195-226 1012-2443 50:1-2<195 2007 50 10472 https://doi.org/10.1007/s10472-007-9067-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10472-007-9067-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hartmann Sven Information Science Research Centre, Dept. of Information Systems, Massey University, Palmerston North, New Zealand aut NATIONALLICENCE 700 1- Köhler Henning Information Science Research Centre, Dept. of Information Systems, Massey University, Palmerston North, New Zealand aut NATIONALLICENCE 700 1- Link Sebastian Information Science Research Centre, Dept. of Information Systems, Massey University, Palmerston North, New Zealand aut NATIONALLICENCE 773 0- Annals of Mathematics and Artificial Intelligence Springer Netherlands 50/1-2(2007-06-01), 195-226 1012-2443 50:1-2<195 2007 50 10472 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer