On Prudent Bravery and Other Abstractions

A special class of partial stable models, the intrinsic ones, is singled out for consideration, and attention is drawn to the largest one, which we designate as the prudently brave one. It is the largest partial stable model that is compatible with every partial stable model. As such, it is an object of natural interest. Its existence follows from general properties of monotonic functions, so it is a robust notion. The proofs given concerning intrinsic stable models are not new, but they appeared earlier in quite different contexts. What we do, essentially, is call the attention of the logic programming and non-monotonic reasoning community to them. We further show the entire development fits into the bilattice framework presented in [5], and thus applies very generally. Finally we show that extending logic programming machinery to allow embedded implications does not essentially change matters: stable model semantics, including the notion of a prudently brave one, continues to apply.