Object Identity and Query Equivalence

Abstract The equivalence problem is studied for programs specifying queries and database restructurings in models using object identity. We use the family of ILOG langauges, which captures essential features of several data restructuring languages in the theoretical and applied literature. ILOG uses a mechanism based on Skolem functors for “inventing” or “creating” object identifiers (OIDs). Two notions of equivalence are articulated: under exposed equivalence the Skolem terms forming created OIDs are exposed; under obscured equivalence these terms are “replaced” with “new’, uninterpreted OIDs. In general, e.g., if either negation or recursion is present, both forms of equivalence are undecidable. In the case of nrecILOG, which can be viewed as unions of conjunctive queries with OID creation, exposed equivalence is decidable. The decidability of obscured equivalence for nrecILOG remains open, but it is shown here to be decidable for a broad class of programs which satisfy the property of isolated OID creation .