# Definition:Propositional Logic

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## 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** (as are its synonyms) 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

- 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): $\S \text{II}.7$: Sentential calculus (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*... (previous) ... (next): Chapter $1$: Introduction: $\S 1.2$: Propositional and predicate calculus - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1$: Propositional Logic - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**logic** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**logic** - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (next): $\S 2$: Propositional Logic: Formulas, Models, Tableaux