Approbation is a formal word that refers to praise or approval.

// Their plan to rewild portions of the city’s parks has won the approbation of the mayor.

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“That’s not to say that all slang terms end up on the ash heap of history. Some of them break out and become incredibly popular. The most successful by far is ‘OK,’ which has become a universal means for expressing approbation. OK has been adopted into many other languages, and it may be the most widely used expression on the planet.” — Roger Kreuz, Psychology Today, 16 Feb. 2024

Approbation is similar in meaning to approval, and it is also very close to approval etymologically. Both words trace back to the Latin verb approbare, which means “to prove” or “to approve.” Approbation meant “proof” when it first appeared in English in the 1300s, and by the early 1500s it had come to refer to the act of formally or officially approving something, a sense it still retains in certain church-related contexts. Today, however, we mostly use approbation in the looser sense of “approval, admiration, or praise.” The related verb approbate means “to approve or sanction,” and the adjective approbatory means “expressing approval or commendation.”