Definition:Literal

Definition

A literal is either:

an atom $p$ of propositional logic, that is, a statement, or

the negation $\neg p$ of an atom $p$.

In the language of propositional logic, these correspond to:

a letter $p$;

the WFF $\neg p$, where $p$ is a letter.

Positive Literal

A positive literal is an atom $p$ of propositional logic.

Negative Literal

A negative literal is the negation $\neg p$ of an atom $p$ of propositional logic.

Also known as

It is also known as a basic statement or basic sentence.

Some sources refer to it as an atom.

When discussing the (formal) language of propositional logic, this can be referred to as a basic WFF.

Sources

• 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{II}$: 'AND', 'OR', 'IF AND ONLY IF': $\S 5$: Exercises, Group $\text{III}$
• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Appendix $\text{A}$: Normal Forms
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): literal: 2.
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.9$: Finished Sets
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.6.1$: Definition $2.57$