Universal (and Existential) Nulls

03/05/2018
by   Gösta Grahne, et al.
0

Incomplete Information research is quite mature when it comes to so called existential nulls, where an existential null is a value stored in the database, representing an unknown object. For some reason universal nulls, that is, values representing all possible objects, have received almost no attention. We remedy the situation in this paper, by showing that a suitable finite representation mechanism, called Star Cylinders, handling universal nulls can be developed based on the Cylindric Set Algebra of Henkin, Monk and Tarski. We provide a finitary version of the cylindric set algebra, called Cylindric Star Algebra, and show that our star-cylinders are closed under this algebra. Moreover, we show that any First Order Relational Calculus query over databases containing universal nulls can be translated into an equivalent expression in our cylindric star-algebra, and vice versa, in time polynomial in the size of the database. The representation mechanism is then extended to Naive Star Cylinders, which are star-cylinders allowing existential nulls in addition to universal nulls. For positive queries (with universal quantification), the well known naive evaluation technique can still be applied on the existential nulls, thereby allowing polynomial time evaluation of certain answers on databases containing both universal and existential nulls. If precise answers are required, certain answer evaluation with universal and existential nulls remains in coNP. Note that the problem is coNP-hard, already for positive existential queries and databases with only existential nulls. If inequalities (x_i≈ x_j) are allowed, reasoning over existential databases is known to be Π^p_2-complete, and it remains in Π^p_2 when universal nulls and full first order queries are allowed.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/19/2023

Work-Efficient Query Evaluation with PRAMs

The paper studies query evaluation in parallel constant time in the PRAM...
research
07/22/2017

Possible and Certain Answers for Queries over Order-Incomplete Data

To combine and query ordered data from multiple sources, one needs to ha...
research
02/13/2019

Counting Answers to Existential Questions

Conjunctive queries select and are expected to return certain tuples fro...
research
07/09/2020

Universal Algebra in UniMath

We present an ongoing effort to implement Universal Algebra in the UniMa...
research
01/19/2018

Computing Possible and Certain Answers over Order-Incomplete Data

This paper studies the complexity of query evaluation for databases whos...
research
02/22/2022

Relational Algebra and Calculus with SQL Null Values

The logic of nulls in databases has been subject of investigation since ...
research
03/04/2023

Locally universal C*-algebras with computable presentations

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds in...

Please sign up or login with your details

Forgot password? Click here to reset