View determinacy for preserving selected information in data transformations

When transforming data one often wants certain information in the data source to be preserved, i.e., we identify parts of the source data and require these parts to be transformed without loss of information. We characterize the preservation of selected information in terms of the notions of invertibility and query preservation, in a setting when transformations are specified as a view V (a set of queries), and source information is selected by a query Q. We investigate the problem for determining whether transformations V preserve the information selected by Q. (1) We show that the notion of invertibility coincides with view determinacy studied for query rewriting. (2) We establish the undecidability of the problem when either Q or V is in DATALOG or first-order logic, for invertibility and query preservation. (3) When Q and V are conjunctive queries (CQ), the problem is as hard as view determinacy for CQ queries and CQ views, an open problem. Nevertheless, we provide complexity bounds of the problem, either in PTIME or NP-complete, when V ranges over subclasses of CQ (i.e., SP, SC, PC), and when Q is assumed to be a minimal CQ query or not. (4) We show that CQ is complete for L-to-CQ rewriting when L is SP, SC or PC, i.e., every CQ query can be rewritten in terms of SP, SC or PC views using a query in CQ.