A Bag-based Data Model with Global Conditions for Incomplete Information

A Bag-based Data Model with Global Conditions for Incomplete Information Akinari YAMAGUCHI†, Shougo SHIMIZU††, Yasunori ISHIHARA†, and Toru FUJIWARA† † Graduate School of Information Science and Technology, Osaka University 1–5 Yamadaoka, Suita, Osaka, 565–0871 Japan †† Department of Computer and Media Technologies, Hiroshima City University 3–4–1 Ozuka-higashi, Asaminami-ku, Hiroshima, 731–3194 Japan Abstract In our previous work, we proposed a data model, called V-bags, for representing incomplete information on bags of tuples. This paper proposes a supermodel of V-bags, called GV-bags, which are V-bags augmented by global conditions. Global conditions restrict assignments over variables in V-bags. Then, the closure properties of six operations, selection, projection, union, product, difference and unique, and their inverses on these models under both closed world assumption (called CWA) and open world assumption (called OWA) are investigated. We obtain that unique on V-bags is closed under CWA, but it under OWA and its inverse on V-bags is not closed under either CWA or OWA. It is shown that inverse of product under CWA, inverse of selection under OWA and inverse of unique under CWA are closed on GV-bags although they are not closed on V-bags. The others are the same as those on V-bags.