A third extension of mathematical logic involves formalizing the notion of context [McCarthy, 1993]. Notice that when logical theories are used in human communication and study, the theory is used in a context which people can discuss from the outside. If computers are to have this facility and are to work within logic, then the ``outer'' logical language needs names for contexts and sentences giving their relations and a way of entering a context. Clearly human-level AI requires reasoning about context.
Human-level AI also requires the ability to transcend the outermost context the system has used so far. Besides in [McCarthy, 1993], this is also discussed in Making Robots Conscious of their Mental States [McCarthy, 1996].
Further work includes [Buvac, 1996] and [Buvac et al., 1995].