Is it fine if I use "define A B" rather than "define A as B"?

Question

The textbook I have been reading uses the sentence:

"As in the discussion of state augmentation in Section 1.4, it is intuitively clear that we should define a new system whose state at time k is the set of all variables the knowledge of which can be of benefit to the controller when making the kth decision."

Getting rid of some trivial parts of the sentence, we get

"We should define a new system whose state at time k is the set of all variables the knowledge of which can be of benefit to the controller when making the kth decision."

Since "whose state at time k is the set of all variables" is just the modifier to "a new system", and since "of which can be of benefit to the controller when making the kth decision" is also the modifier to "the knowledge", we can reduce the sentence to

"We should define a new system the knowledge."

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Now, I was wondering why the author did not write "We should define a new system as the knowledge."

Is the phrase of "define A B" equivalent to one of "define A as B"?

Answer 1

we can reduce the sentence to

"We should define a new system the knowledge."

No, that's wrong. You can reduce the original sentence to three statements:

1. We should define a new system;
2. The state of the system (not the system itself) will be a set of variables;
3. The variables included in the set will be those that the controller can use in making a decision.

Is the phrase of "define A B" equivalent to one of "define A as B"?

No.

Answer 2

In geometry, for instance, a line AB would be a line from A to B, and the question would be to define that line. This would not be the same as defining A in relation to B.