Universal finiteness and satisfiability (extended abstract)

• Authors: Inderpal Singh Mumick;Oded Shmueli
• Venue: PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
• Year: 1994

The problem of determining whether, for every extensional database, a given predicate in a given program has a finite number of derivations is called the universal finiteness problem. The problem of determining whether a given predicate in a given program has a non-empty extension for some extensional database is called the satisfiability problem. We show that the universal finiteness problem can be reduced to the satisfiability problem. Thus all decidability results for satisfiability can be applied to universal finiteness—for example, we can infer that the universal finiteness problem is decidable for Datalog extended with negation on base predicates. The satisfiability problem can be easily reduced to the universal finiteness problem, so that all undecidability results for satisfiability can be applied to universal finiteness. For example we can infer that the universal finiteness problem is undecidable for Datalog extended with stratified negation.Many recursive programs have infinite number of derivations only when ed b relations have data cycles. It is thus of particular interest to study universal finiteness in the presence of acyclicity constraints on the ed b relations. We define acyclicity constraints in terms of non-satisfiability of a specific recursive program. We show that both the problems of universal finiteness and satisfiability of Datalog in the presence of acyclicity constraints (on one or more ed b relations) remain decidable for a language L whenever the problems are decidable for language L in absence of such constraints. We also show that the problems are undecidable for arbitrary constraints expressed in terms of non-satisfiability of a recursive program.