Definition:Semantic Equivalence/Boolean Interpretations/Definition 2
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Definition
Let $\mathbf A, \mathbf B$ be WFFs of propositional logic.
Then $\mathbf A$ and $\mathbf B$ are equivalent for boolean interpretations if and only if:
- $\map v {\mathbf A} = \map v {\mathbf B}$
for all boolean interpretations $v$.
Also see
Sources
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Connectives
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.4$: Logical equivalence and substitution: Definition $2.4.1$
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.3$: Definition $2.26$