On the Translatability of View Updates

We revisit the view update problem and the abstract functional
framework by Bancilhon and Spyratos in a setting where views and
updates are exactly given by functions that are expressible in first-order
logic. We give a characterisation of views and their inverses based on the
notion of definability, and we introduce a general method for checking
whether a view update can be uniquely translated as an update of the
underlying database under the constant complement principle. We study
the setting consisting of a single database relation and two views defined
by projections and compare our general criterion for translatability with
the known results for the case in which the constraints on the database
are given by functional dependencies. We extend the setting to any number
of projective views, full dependencies (that is, egd's and full tgd's) as
database constraints, and classes of updates rather than single updates.