A Model Theoretic Semantics for Multi-level Secure Deductive Databases

Abstract

The impetus for our current research is the need to provide an adequate framework for belief reasoning in multi-level secure (MLS) databases. We demonstrate that a prudent application of the concept of inheritance in a deductive database setting will help capture the notion of declarative belief and belief reasoning in MLS databases in an elegant way. In this paper, we show that these concepts can be captured in a F-logic style declarative query language, called MultiLog, for MLS deductive databases for which a model theoretic semantics exists. This development is significant from a database perspective as it now enables us to compute the semantics of MultiLog databases in a bottom-up fashion. The semantics developed here is reminiscent of the stable model semantics of logic programs with negation. We also define a bottom-up procedure to compute unique models of stratified MultiLog databases. Finally, we also establish the equivalence of MultiLog’s three logical characterizations — model theory, fixpoint theory and proof theory.

Research supported in part by a grant from the National Science Foundation.

Research completed while the author was visiting Mississippi State University in October 2000, while she was on sabbatical at the National University of Singapore.