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predicate (something) on (something else)
To base, establish, or found something on some argument, fact, circumstance, etc. Often used in passive constructions. You shouldn't predicate your decision on the reputation of his previous employer. Our country's legal system is predicated on the assumption that all men and women are equal in the eyes of the law.
predicate something (up)on something
to base something on something. There is no need to predicate my promotion upon the effectiveness of my secretary! You can hardly predicate the picnic on the weather, can you?