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Belnap-Dunn logic and query answering in inconsistent databases with null values

C. A. Middelburg

TL;DR

An expansion of first-order Belnap-Dunn logic, called BD^{\supset,F}_{\bot}, and an application of this logic in the area of relational database theory, taking into account that a database may be an inconsistent database and/or a database with null values.

Abstract

This paper concerns an expansion of first-order Belnap-Dunn logic, named $\mathrm{BD}^{\supset,\mathsf{F}}$, and an application of this logic in the area of relational database theory. The notion of a relational database, the notion of a query applicable to a relational database, and several notions of an answer to a query with respect to a relational database are considered from the perspective of this logic, taking into account that a database may be an inconsistent database or a database with null values. The chosen perspective enables among other things the definition of a notion of a consistent answer to a query with respect to a possibly inconsistent database without resort to database repairs. For each of the notions of an answer considered, being an answer to a query with respect to a database of the kind considered is decidable.

Belnap-Dunn logic and query answering in inconsistent databases with null values

TL;DR

An expansion of first-order Belnap-Dunn logic, called BD^{\supset,F}_{\bot}, and an application of this logic in the area of relational database theory, taking into account that a database may be an inconsistent database and/or a database with null values.

Abstract

This paper concerns an expansion of first-order Belnap-Dunn logic, named , and an application of this logic in the area of relational database theory. The notion of a relational database, the notion of a query applicable to a relational database, and several notions of an answer to a query with respect to a relational database are considered from the perspective of this logic, taking into account that a database may be an inconsistent database or a database with null values. The chosen perspective enables among other things the definition of a notion of a consistent answer to a query with respect to a possibly inconsistent database without resort to database repairs. For each of the notions of an answer considered, being an answer to a query with respect to a database of the kind considered is decidable.
Paper Structure (9 sections, 7 theorems, 18 equations, 2 tables)

This paper contains 9 sections, 7 theorems, 18 equations, 2 tables.

Table of Contents

  1. Introduction
  2. The Language of ${\mathrm{BD}^{ \mathbin{\supset},{\mathsf{F}}}}$
  3. Truth and Logical Consequence in ${\mathrm{BD}^{ \mathbin{\supset},{\mathsf{F}}}}(\mathit{\Sigma})$
  4. A Proof System for ${\mathrm{BD}^{ \mathbin{\supset},{\mathsf{F}}}}(\mathit{\Sigma})$
  5. Covering Terms with an Indeterminate Value
  6. Relational Databases Viewed through ${\mathrm{BD}^{ \mathbin{\supset},{\mathsf{F}}} _{ \bot}}$
  7. Query Answering Viewed through ${\mathrm{BD}^{ \mathbin{\supset},{\mathsf{F}}} _{ \bot}}$
  8. The Views on Null Values in Databases
  9. Concluding Remarks

Key Result

proposition thmcounterproposition

Let $\mathbf{A}$ be a structure of ${\mathrm{BD}^{ \mathbin{\supset},{\mathsf{F}}}}(\mathit{\Sigma})$ such that $\mathcal{U}\sp\mathbf{A}$ is finite, and let $\alpha$ be an assignment in $\mathbf{A}$. Then, it is decidable whether, for a formula $A \in \mathcal{F}\!\!\mathit{orm}(\mathit{\Sigma})$,

Theorems & Definitions (13)

  • proposition thmcounterproposition
  • proof
  • theorem thmcountertheorem
  • proof
  • theorem thmcountertheorem
  • proof
  • corollary thmcountercorollary
  • theorem thmcountertheorem
  • proof
  • theorem thmcountertheorem
  • ...and 3 more