Definition:Language of Propositional Logic/Alphabet/Sign/Connective

Definition

The signs of the language of propositional logic include the connectives:

\(\ds \bullet \ \ \)

\(\ds \land\)

\(:\)

\(\ds \)the conjunction sign\(\)

\(\ds \bullet \ \ \)

\(\ds \lor\)

\(:\)

\(\ds \)the disjunction sign\(\)

\(\ds \bullet \ \ \)

\(\ds \implies\)

\(:\)

\(\ds \)the conditional sign\(\)

\(\ds \bullet \ \ \)

\(\ds \iff\)

\(:\)

\(\ds \)the biconditional sign\(\)

\(\ds \bullet \ \ \)

\(\ds \neg\)

\(:\)

\(\ds \)the negation sign\(\)

\(\ds \bullet \ \ \)

\(\ds \top\)

\(:\)

\(\ds \)the tautology sign\(\)

\(\ds \bullet \ \ \)

\(\ds \bot\)

\(:\)

\(\ds \)the contradiction sign\(\)

These comprise:

• The nullary connectives $\top$ and $\bot$, representing the canonical tautology and contradiction, respectively

• The unary connective $\neg$, representing negation

• The binary connectives $\land, \lor, \implies$ and $\iff$, representing, respectively, conjunction, disjunction, implication and biconditional.

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $1$ Formation Rules
• 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.2$: Propositional formulas
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.2$: Syntax of Propositional Logic
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.1.1$: Definition $2.1$