Reiter’s logic for default reasoning
Let (F, D) be a theory and S a set of sentences. Then G(S) is the smallest set G of sentences, such that the following hold:
1. F ? G
2. G = Th(G)
3. For all a : b1, b2, ..., bn / g ? D:
If a ? G and for all j: ?bj ? S, then g ? G.
A set of sentences E is an extension of a theory (F, D) if E = G(E).