A Formalisation of Logic Databases and Integrity Constraints

Abstract

This paper presents a meta-level/object-level framework (MOF) for the formalisation of logic databases (LDBs). The MOF is based on first order logic and thus benefits and employs many of the properties and results of that logic, eg. rich representation language, well-defined semantics, resolution theorem proving, etc. The meta theory in the MOF provides a sound formalisation environment in which we can tackle many as yet open LDB problems such as capturing the “true intended meaning” of the notion of integrity constraints where they contain subtle presumptions in their natural language statements, formalisation and enforcement of “dynamic” integrity constraints within the same framework as their static counter-parts, declarative representation of concepts of database update operations, query evaluation and optimisation, and control of the reasoning in the underlying LDB theory (i.e. the object theory of the MOF). Finally, from implementation view point, one can implement useful classes of LDBs formalised in the MOF within a suitable logic programming environment such as METAPROLOG or GODEL.