What is meant by "known" in "A knowledge-base exhibits complete knowledge if and only if, for every $P$, $P$ or $\neg P$ is known"? I have a question as to what it means for a knowledge-base to be consistent and complete. I've been looking into non-monotonic logic and different formalisms for it from the book &quot;Knowledge Representation and Reasoning&quot; by Hector Levesque and Ronald J. Brachman, but something is confusing me.
They say:

We say a KB exhibits consistent knowledge iff there is no sentence $P$ such that both $P$ and $\neg P$ are known. This is the same as requiring the KB to be satisfiable. We also say that a KB exhibits complete knowledge iff for every $P$ (within its vocabulary) $P$ or $\neq P$ is known

They then seem to suggest that by &quot;known&quot; they mean &quot;entailed&quot;. They say

In general, of course, knowledge can be incomplete. For example, suppose KB consists of a single sentence ($P$ or $Q$). Then KB does not entail either $P$ or $\neg P$, and so exhibits incomplete knowledge.

But when dealing with sets of sentences, I usually see these terms as being defined w.r.t. derivability and not entailment.
So my question is, what exactly do these authors mean by &quot;known&quot; in the above quotes?
Edit: this post helped clarify things.
It seems that they are stating that a knowledge base is consistent if and only if it never asserts the truth of both the truth and the negation of a particular P. In other words, a knowledge base is consistent if it never contradicts itself. Their definition allows incomplete knowledge bases to be considered consistent; by their definition, an empty knowledge base is still considered a consistent one.