Relational Semantics for Databases and Predicate Calculus

TL;DR

This paper develops a mathematically rigorous theory of relations with non-numerical indexes and introduces an alternative semantics for predicate calculus, making it suitable for relational database query languages.

Contribution

It introduces a new theory of relations with non-numerical indexes and an alternative semantics for predicate calculus tailored for database applications.

Findings

Defines operations on relations suitable for databases

Develops a new semantics for predicate calculus

Makes classical predicate calculus applicable as a query language

Abstract

The relational data model requires a theory of relations in which tuples are not only many-sorted, but can also have indexes that are not necessarily numerical. In this paper we develop such a theory and define operations on relations that are adequate for database use. The operations are similar to those of Codd's relational algebra, but differ in being based on a mathematically adequate theory of relations. The semantics of predicate calculus, being oriented toward the concept of satisfiability, is not suitable for relational databases. We develop an alternative semantics that assigns relations as meaning to formulas with free variables. This semantics makes the classical predicate calculus suitable as a query language for relational databases.