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Independent claim:

X is a positive number;

there are three variables: A, B, and C;

Y happens if A <= X, B <= X, and C <= X;

Dependent claim:

C is restricted to always equal zero.

If C is restricted to always equal zero, then the condition C <= X is always true, which is equivalent to not having this condition to begin with.

Is this a valid dependent claim? It seems to be broader than the independent claim

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3 Answers 3

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I would say it's not a valid dependent claim. The claim it depends on specifies that C is a variable. If you then fix C to zero, it becomes a constant, which is the opposite of a variable. A dependent claim can only narrow elements, it can't change them into different things.

One can certainly form paradoxes in claimese because it is based on the English language which falls short of what mathematicians call a "formal system", which can be made paradox-free. (Formal systems have been built and are distributed with various tools called "interactive theorem provers", for example, Coq.)

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  • Ok, what if in the independent claim, the word "variable" is removed, so that the values A, B, C can be predefined constants also?
    – Bear Bile Farming is Torture
    Commented Aug 24 at 16:34
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    More generally, we can ask what is the proper set relation between a machine M1 where X happens if A and a machine M2 where X happens if B. Suppose A is a subset of B. Now M2 could probably be a dependent version of M1 because M2 does X when A -and- X when B. Note that we had to broaden the condition to narrow the claim! I believe a similar problem arises with negative limitations.
    – bhuff36
    Commented Aug 24 at 16:47
  • So to clarify, are you saying that the dependent claim in my question could indeed be a valid if the word "variable" is removed?
    – Bear Bile Farming is Torture
    Commented Aug 24 at 16:56
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The answer to the title of the question is a proper dependent is by definition narrower than the claim it depends from. Period.

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In your example the dependent claim is not a dependent claim.

If the examiner does his/her job properly then they will raise a clarity objection regarding the dependency of your claim. As by definition a dependent claim needs to contain all features of the independent claim, and as you pointed out your "dependent" claim is the same as not having the feature (i.e. the condition c<=x), which ends up being broader then the claim it depends on. Thus, the dependency becomes unclear for the cases where in the independent claim, C is chosen as being bigger than zero.

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