Universal (and Existential) Nulls
G\"osta Grahne, Ali Moallemi

TL;DR
This paper introduces a novel finite representation called Star Cylinders for handling universal nulls in databases, establishing their algebraic properties and translating queries efficiently, thus advancing incomplete information research.
Contribution
It develops the Cylindric Star Algebra for universal nulls and demonstrates polynomial-time query translation and evaluation methods involving universal and existential nulls.
Findings
Star Cylinders effectively represent universal nulls.
Query translation between first-order calculus and cylindric star-algebra is polynomial.
Evaluation of certain answers remains polynomial, but general reasoning is coNP-hard.
Abstract
Incomplete Information research is quite mature when it comes to so called {\em existential nulls}, where an existential null is a value stored in the database, representing an unknown object. For some reason {\em universal nulls}, that is, values representing {\em all} possible objects, have received almost no attention. We remedy the situation in this paper, by showing that a suitable finite representation mechanism, called {\em Star Cylinders}, handling universal nulls can be developed based on the {\em Cylindric Set Algebra} of Henkin, Monk and Tarski. We provide a finitary version of the cylindric set algebra, called {\em Cylindric Star Algebra}, and show that our star-cylinders are closed under this algebra. Moreover, we show that any {\em First Order Relational Calculus} query over databases containing universal nulls can be translated into an equivalent expression in our…
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