Formalizing a constraint deductive database language based on hereditary harrop formulas with negation

Abstract

In this paper, we present an extension of the scheme HH(C) (Hereditary Harrop formulas with Constraints) with a suitable formulation of negation in order to obtain a constraint deductive database query language. In addition to constraints, our proposal includes logical connectives (implication and quantifiers) for defining databases and queries, which altogether are unavailable in current database query languages. We define a proof theoretic semantic framework based on a sequent calculus, that allows to represent the meaning of a database query by means of a derived constraint answer in the sense of CLP. We also introduce an appropriate notion of stratification, which provides a starting point for suitable operational semantics dealing with recursion and negation. We formalize a fixed point semantics for stratifiable databases, whose fixpoint operator is applied stratum by stratum. This semantics is proved to be sound and complete with respect to derivability in the sequent calculus, and it provides the required support for actual implementations, as the prototype we have developed already and introduce in this paper.