Exclusion as the meaning of a sentence

Buddhist Pramāṇavādins maintain that a word, such as "cow" does not denote an external referent, but the exclusion of whatever is not a non-cow. But can this thesis also explain how are sentence-meanings conveyed? Kumārila claims that they can, because exclusion, if applied to sentence-meanings, contradicts one of the very basic tenets of the Buddhist thought, i.e., instantaneity.
Discussing the sentence "the cow is white", Kumārila writes (ŚV vākyādhikaraṇa 20cd-21ab):

If the notion of a cow would continue to exist at the moment of the arousal of the notion of white |
then, it would be excluded from the other [notions] or joined with this (notion of "white") [but it cannot continue to exist, due to momentariness] ||
(yadi dhriyeta gobuddhiḥ śuklabuddhijanikṣaṇe || 20 || tato 'nyābhyo nivarteta saṃsṛjeta tathānayā |)

Pārthasārathi Miśra's commentary is even clearer:

In the sentence "the cow is white" the notion born out of the word "cow" extends to all cows, white, black, etc. If the arousal of the notion "white", produced by the word white would last long enough, then it could be connected to the notion "cow" and it could be excluded from the other notions of the individual black etc. But it does not last, because it is instantaneous.
(gauḥ śuklaḥ ity atra gośabdajanitā buddhiḥ sarvagavīṣu śuklakṛṣṇādiṣu prasṛtā yadi śuklaśabdajanitaśuklabuddhijananaṃ yāvad dhriyeta tatas tayā saṃsṛjyeta anyābhyo vā kṛṣṇādivyaktibuddhibhyo vyavacchidyeta na tu sā dhriyate kṣaṇikatvād iti.)

In other words, apoha might work for single words, but in the case of a sentence, one should imagine that "the cow is white" means the exclusion of whatever non-non-cow is not non-white. But how can the notion of a non non-cow last long enough to exclude whatever is not non-white?