Definition:Logical Not/Boolean Interpretation
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Definition
Let $\mathbf A$ be a propositional formula.
Let $\neg$ denote the negation operator.
The truth value of $\neg \mathbf A$ under a boolean interpretation $v$ is given by:
- $\map v {\neg \mathbf A} = \begin{cases}
\T & : \map v {\mathbf A} = \F \\ \F & : \map v {\mathbf A} = \T \end{cases}$
Sources
- 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{II}$: 'AND', 'OR', 'IF AND ONLY IF': $\S 6 \ (2)$
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.3$: Boolean interpretations: Figure $2.7$
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.5$: Semantics of Propositional Logic