Fangzhen Lin and Yoav Shoham defined a propositional nonmonotonic logic which uses two independent modal operators. One of them represents minimal knowledge, the other is related to the ideas of justification (as understood in default logic) and of negation as failure. We describe a simplified version of that system, show how quantifiers can be included in it, and study its relation to circumscription and default logic, to logic programming, and to the theory of epistemic queries developed by Hector Levesque and Ray Reiter.

PS

In Gabbay, D.M. and Hogger, C.J. and Robinson, J.A., editors, Handbook of Logic in AI and Logic Programming, 70, 53--72, 1994. Oxford University Press.

@INCOLLECTION{lif93e, title={Minimal Belief and Negation as Failure}, author={Vladimir Lifschitz}, booktitle={Handbook of Logic in AI and Logic Programming}, volume={70}, journal={Artificial Intelligence}, editor={Gabbay, D.M. and Hogger and C.J. and Robinson and J.A.}, publisher={Oxford University Press}, pages={53--72}, url="http://www.cs.utexas.edu/users/ai-lab/pub-view.php?PubID=971", year={1994} }