Decidability and expressiveness aspects of logic queries

TL;DR: In this paper, the problem of determining containment, equivalence, and satisfiability of logic-based queries over relational databases is addressed, and it is shown that determining safety and literal redundancy are undecidable problems.

Abstract: This paper addresses some basic problems regarding logic programming based queries over relational databases. We re-examine the query classes H and YE+ defined by Chandra and Harel [2] We define H+ and YE++ which differ from H and YE+ in that the use of equality (=) and inequality (≠) is prohibited. We show that H+ is more expressive than YE++ and that any H+ program can be transformed into an equivalent H+ program containing a single recursive predicate without using the equality or inequality operators. As a corollary we obtain a fixpoint formula characterization of H+ queries.We consider the problems of determining containment, equivalence, and satisfiability of logic based queries. The containment and equivalence problems addressed here extend the work of Aho, Sagiv and Ullman on relational queries [1] and Papadimitrious on Prolog [10]. As corollaries we show that determining safety and literal redundancy are both undecidable problems.