'When I closed my eyes the cat was sitting on the table; when I opened my eyes I found it sitting on the chair; therefore I conclude that the cat must have moved from the table to the chair while my eyes were closed.' According to classical Indian philosophy, which means of knowledge is used in the above argument?

The knowledge here comes through arthapatti, postulation.

Two observed facts clash: the cat was on the table, then on the chair, unseen in between.

The only way to reconcile them is to postulate that the cat moved while the eyes were closed.

A fact is assumed because without it the observed facts cannot be explained.

This necessary supposition to remove an apparent conflict is arthapatti.