Definition:Language of Propositional Logic/Alphabet/Sign
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Definition
The signs of the language of propositional logic come in two categories:
Brackets
\(\ds \bullet \ \ \) | \(\ds (\) | \(:\) | \(\ds \)the left bracket sign\(\) | |||||||||||
\(\ds \bullet \ \ \) | \(\ds )\) | \(:\) | \(\ds \)the right bracket sign\(\) |
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): $\S 2.1$: 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
- 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.3$: Propositional logic as a formal language