15.00 - Definitions of Terms - Teradata Database

Teradata Database Design

prodname
Teradata Database
vrm_release
15.00
category
User Guide
featnum
B035-1094-015K

Definitions of Terms

Before proceeding further, some definitions for terms used in predicate logic and the predicate calculus are in order.

 

Term

Definition

Assertion

See “Proposition”.

Existential quantifier

The symbolic quantifier of predicate logic, signifying the logically equivalent English language phrases “for some,” “for any,” and “there exists.”

Identity predicate

The symbolic operator = of predicate logic, signifying the logically equivalent English language phrases “is identical to” or “is equal to.”

Inference rules

The rule set of a formal system that determines the steps of reasoning that are valid for proving logical propositions.

Predicate

A truth-valued function.

The attributes of a relation (columns), as well as the relation heading (relation variable) itself, can be represented formally as logical predicates.

This is true whether an explicit constraint is defined over the column or not, because when no explicit constraint is defined, the implicit constraint specified by the data type for the column specifies its minimum, essential, constraint. You cannot, for example, insert the character string ‘character string’ into a column typed as INTEGER without first converting the string into an integer value.

This type of constraint is known as a domain constraint (see “Domain Constraints” on page 633).

Predicate calculus

The set of inference rules by which propositions in predicate logic are proven.

Predicate logic

The study of statement validity using the truth-functional operators of the propositional calculus, the universal and existential quantifiers, and the identity predicate.

Proposition

An assertion that can be proven unequivocally to be either true or false.

In a relational table, or relation variable, all rows are assumed to be true propositions by default, because if they were false, they would have been prevented from entry in the database by the various integrity constraints, both implicit and explicit, defined on that database. Each proposition (tuple) in a relation is an instantiation of its relation variable predicate that evaluates to TRUE.

This important property is sometimes called the Closed World Assumption (see “The Closed World Assumption” on page 630).

Logical propositions have wide application throughout computer science. See Hoare (2003) for a historical review.

Truth-valued function

A function that evaluates unequivocally to either TRUE or FALSE.

Universal quantifier

The symbolic quantifier of predicate logic, signifying the English language phrase “for all.”