# Definition:Propositional Logic

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## Contents

## Definition

**Propositional logic** is a sub-branch of symbolic logic in which the truth values of propositional formulas are investigated and analysed.

The atoms of propositional logic are simple statements.

There are various systems of propositional logic for determining the truth values of propositional formulas, for example:

- Natural deduction is a technique for deducing valid sequents from other valid sequents by applying precisely defined proof rules, each of which themselves are either "self-evident" axioms or themselves derived from other valid sequents.

- The Method of Truth Tables, which consists of the construction of one or more truth tables which exhaustively list all the possible truth values of all the statement variables with a view to determining the required answer by inspection.

## Also known as

As **propositional logic** is such a mouthful and takes so long to write, some authors succumb to the temptation to abbreviate it by referring to it more-or-less consistently as **PropLog**.

**Propositional logic** is also referred to as:

**zeroth order logic**(where**first order logic**is predicate logic)**Propositional calculus****Sentential calculus****Theory of deduction**

## Also see

- Definition:Elementary Valid Argument Form
- Definition:Language of Propositional Logic
- Results about
**propositional logic**can be found here.

## Sources

- 1946: Alfred Tarski:
*Introduction to Logic and to the Methodology of Deductive Sciences*(2nd ed.) ... (previous) ... (next): $\S \text{II}.6$: Logical Constants (footnote) - 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): $\S 2.1$: Propositions and their Relations - 1982: P.M. Cohn:
*Algebra Volume 1*(2nd ed.) ... (next): Chapter $1$: Sets and mappings: $\S 1.1$: The need for logic - 1993: M. Ben-Ari:
*Mathematical Logic for Computer Science*(1st ed.) ... (previous) ... (next): $\S 1.2$: Propositional and predicate calculus - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1$: Propositional Logic - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (next): $\S 2$: Propositional Logic: Formulas, Models, Tableaux