An algebra of layered complex preferences

Preferences allow more flexible and personalised queries in database systems. Evaluation of such a query means to select the maximal elements from the respective database w.r.t. to the preference, which is a partial strict-order. Often one requires the additional property of negative transitivity; such a strict weak order induces equivalence classes of "equally good" tuples, arranged in layers of the order. We extend our recent algebraic, point-free, calculus of database preferences to cope with weak orders. Since the approach is completely first-order, off-the-shelf automated provers can be used to show theorems concerning the evaluation algorithms for preference-based queries and their optimisation. We use the calculus to transform arbitrary preferences into layered ones and present a new kind of Pareto preference as an application