Definition:Semantic Equivalence/Boolean Interpretations/Definition 2

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

• Definition:Semantic Consequence (Boolean Interpretations)
• Definition:Logical Equivalence

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 $2.26$