What is faith?

In Christian theology, faith is normally considered to be a necessary condition of salvation. I've discussed how, in Reformed theology, regeneration is more fundamental than faith. Regeneration is the source of faith (although faith also requires a mental object). 

One component of faith is belief. But that's ambiguous. Epistemologists distinguish between occurrent belief and dispositional belief. We aren't conscious of everything we know or believe. In that respect, belief is very similar to memory. It's available. On tap. Occurrent beliefs come and go but dispositional belief is relatively constant–although some beliefs undergo change. Even at a dispositional level, you don't believe all the same things throughout life. 

In that respect, belief has a hypothetical dimension. In part a matter of how you'd think and respond in case you found yourself in a particular situation. The situation brings outlook out to the fore. 

So, for instance, does a Christian cease to be a believer when he sleeps? He may have some occurrent beliefs in his dreams, but generally, his beliefs, including his Christian beliefs, are unconscious or subconscious when he sleeps. 

And even when he's awake, he isn't continuously aware of his Christian beliefs. More often, his Christian beliefs lie behind some of his choices and actions rather than in the forefront. They exert a subconscious influence.

This distinctions have some possible bearing on the nature of exclusivism. Insofar as salvation is contingent on orthodox beliefs, that generally operates at the dispositional level rather than occurrently.