First off, know that despite what some people hope, an AI singularity being a solution to the problem of mortality is not really compatible with materialism combined with current understanding of physics. (This isn't really specific to AI, but AI singulatatians seem to have a fairly high rate of expecting something like that.)

Second of all, check out miri. Their work on AI safety is pretty interesting. There are also other groups.

Recently they came up with a formalism for assigning "probabilities" to statements which might be implied by things one knows, or might not be, but due to computational resources, one hasn't found out yet. It seems quite interesting.