In Artificial Intelligence: a Modern Approach, when it talks about strategies to improve efficiency of resolution inference(section 9.5.6), it says selecting the set of support and resolving one of elements in it first are helpful. But I cannot understand the way it select the set of support and why.

The original excerpt as follows:

Set of support: Preferences that try certain resolutions first are helpful, but in general it is more effective to try to eliminate some potential resolutions altogether. For example, we can insist that every resolution step involve at least one element of a special set of clauses—the set of support. The resolvent is then added into the set of support. If the set of support is small relative to the whole knowledge base, the search space will be reduced dramatically.

We have to be careful with this approach because a bad choice for the set of support will make the algorithm incomplete. However, if we choose the set of support S so that the remainder of the sentences are jointly satisfiable, then set-of-support resolution is complete. For example, one can use the negated query as the set of support, on the assumption that the original knowledge base is consistent. (After all, if it is not consistent, then the fact that the query follows from it is vacuous.) The set-of-support strategy has the additional advantage of generating goal-directed proof trees that are often easy for humans to understand.

What does it mean that the remainder of the sentences are jointly satisfiable? Why could one use the negated query as the set of support?

Thanks in advance, I hope someone could shed some light on it:)

Ps. I'm a English leaner. I may not present this problem very well, and I'm very sorry for that. But I‘m very serious about it and I've try my best to make it as clear as I can. So if you're about to down vote it, please comment below and give me some advice to improve it, I'll be very grateful for that. Thanks again!



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