Logical Queries over Views: Decidability and Expressiveness

TL;DR

This paper identifies a new decidable class of first order logic queries over unary conjunctive views, extending classical results and highlighting boundaries between decidability and undecidability relevant to database applications.

Contribution

It introduces a decidable class of queries over unary conjunctive views that generalizes the Lowenheim class, and explores the limits of expressiveness and undecidability extensions.

Findings

Decidable class over unary conjunctive views generalizes Lowenheim class.

Extensions lead to undecidability.

Potential applications in dependency implication and ontology reasoning.

Abstract

We study the problem of deciding satisfiability of first order logic queries over views, our aim being to delimit the boundary between the decidable and the undecidable fragments of this language. Views currently occupy a central place in database research, due to their role in applications such as information integration and data warehousing. Our main result is the identification of a decidable class of first order queries over unary conjunctive views that generalises the decidability of the classical class of first order sentences over unary relations, known as the Lowenheim class. We then demonstrate how various extensions of this class lead to undecidability and also provide some expressivity results. Besides its theoretical interest, our new decidable class is potentially interesting for use in applications such as deciding implication of complex dependencies, analysis of a restricted class of active database rules, and ontology reasoning.