The landscape of the pramana anupalabdhi accepted by Advaita is a strange one lit up by flashes of understanding. As ever negation is the way to knowledge. The Nyaya school do not accept non-apprehension of existence as a distinct valid means of knowledge holding that it is based on perception.
First though the positive thesis. Here I follow the line laid down by the Vedanta Paribhasa by Dharmaraja Adhvarindra. Put at its simplest it may seem otiose. Looking at a cleared table I can say ‘there is no jug on the table’. There is a non-apprehension of the existence of a jug. This is different from perception in that I cannot perceive what isn’t there. There is no non-jug that I perceive to be not there. I can further add that if there was a jug on the table I would see it. Only perceptible things are of interest here even if the pramana is not based on perception. It is claimed to be an immediate knowledge not delivered by sense perception. It proceeds direct to the mind.
It might be claimed that a vast number of things that are perceptible and tableable are not there so there is very little value in such information. That’s true but it is not the information but the means that is at issue. In any case this pramana is useful when we notice the absence of something that should be there. The book that was on the table is not there when I go to look for it. If the restaurant manager tells the waiter that ‘there is no water on the table’ that non-apprehension of existence is a direction to action.
My previous remarks on this topic can be found by putting ‘anupalabadhi’ in the search box. Notice the incorrect spelling - without spellcheck my English spelling would be no better.