Languages for relational databases over interpreted structures

Michael Benedikt, Leonid Libkin
1997 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '97  
We rework parts of the classical relational theory when the underlying domain is a structure with some interpreted operations that can be used in queries. We identify parts of the classical theory that go through'as before' when interpreted structure is present, parts that go through only for classes of nicely-behaved structures, and parts that only arise in the interpreted case. The rst category includes a number of results on equivalence of query languages, as well as expressive power
more » ... rizations for the active-domain semantics for a variety of logics. The second category includes most of our results on the natural semantics, including results on cases where the natural semantics collapses to the active semantics. While these collapse results have been proved by nonconstructive means for rst-order logic in previous work, we here give a set of algorithms for eliminating unbounded quanti cations in favor of bounded ones. Furthermore, we show these results for a new class of higher-order logics that mix unbounded and bounded quanti cation. We give a set of normal forms for these logics, under special conditions on the interpreted structures. As a by-product, we obtain an elementary proof of the fact that parity test is not de nable in the relational calculus with polynomial inequality constraints.
doi:10.1145/263661.263672 dblp:conf/pods/BenediktL97 fatcat:ry2btuu4mbezpehnajywlmazpy