The affix ṭhak comes in the sense of 'this is whose belief' after the words 1. asti 2. nāsti and 3. diṣṭa,
Thus अस्तिमतिरस्य = आस्तिकः 'who believes that It is' i.e. a here after. मास्तिकः 'whose belief is that there is no Here after', an athiest. दैष्टिकः 'whose belief is that it is fate', a fatalist, दिष्टः = दैव 'fate'.
The affix does not apply in the sense of belief in general, but to a particular sort of belief. Thus परलोकोऽस्ति इति यस्य मतिरस्ति स आस्तिकः, an Astika is he who believes that the Hereafter is. Contrary to him is a नास्तिकः who does not believe in a Hereafter. A person who believes what is demonstrated by proof, and nothing else, may also be called दैष्टिकः 'a positivist'. These various other senses are to be found from dictionary and general literature.,