Proving finite satisfiability of deductive databases

Abstract

It is shown how certain refutation methods can be extended into semi-decision procedures that are complete for both unsatisfiability and finite satisfiability. The proposed extension is justified by a new characterization of finite satisfiability. This research was motivated by a database design problem: Deduction rules and integrity constraints in definite databases have to be finitely satisfiable.

A Hyperresolution-based Proof Procedure and Its Implementation in Prolog

“…In [BM86] we have inves tigated which additional features are required for achieving completeness for both, unsatisfiability as well as finite satisfiability. An extension of our method with these additional features appears to be straightforward.…”

Modal Tableau Systems with Blocking and Congruence Closure

“…An alternative way of achieving this is to use the (ub-δ * )-rule. If this rule is applied eagerly immediately after the application of a witness-creating rule, then this emulates the use of the (δ * )-rule of [7]. E.g., the (δ * )-version of the (¬2)-rule is:…”

Towards intelligent databases

“…Theoretical issues have been investigated (see e.g. [28,29,30,31,65,21,8,48,64,17,18,44,45] for an overview), and experimental deductive database management systems have been and are still implemented (e.g. [54,9,23,26,32,34,51,56,66,33,68,40,52]).…”

“…Instead of emphasizing technical aspects (that are explained in a number of articles and tutorials, e.g. [28,29,30,31,65,21,8,17,18]), we prefer to insist on the goals of the deductive approach to databases.…”

“…[17,18,1,2,4,7,55,57,60,61,67,13]), and how integrity constraints are checked when the database is updated (see e.g. [17,18,15,25,39,43,47,49,53,19]). …”