Nonmonotonic reasoning from conditional knowledge bases with system W

Abstract For nonmonotonic reasoning in the context of a knowledge base $\mathcal {R}$ R containing conditionals form If A then usually B , system P provides generally accepted axioms. Inference solely based on P, however, is inherently skeptical because it coincides with that takes all ranking models into account. System Z uses only unique minimal model and c-inference, realized via complex constraint satisfaction problem, c-representations C-representations constitute subset are obtained by assigning non-negative integer impacts to each conditional summing up, for every world, falsified world. While c-inference license general different sets desirable entailments, first major objective this article present W . fully captures strictly extends both c-inference. Moreover, can be represented single strict partial order worlds over signature We show exhibits further inference properties worthwhile reasoning, like satisfying axioms respecting indifference, avoiding drowning problem. The other main goal provide results our investigations, underlying development W, upper lower bounds used restrict set have taken account realizing bound n − 1 sufficient capturing respect having if there at least one world verifying In contrast previous conjecture number always sufficient, we prove bases requiring an 2 implying no polynomial assigned