Definition:Propositional Logic

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 (where sentential is the adjectival form of sentence)
• 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): $\S \text{II}.7$: 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