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I have seen the following formula when writing an academic article:

To the best of our knowledge, this is the first work that shows how to optimize a non-submodular function for ....

I like this construction in a paper, and I am wondering if there is a way to replace "To the best of our knowledge" by a similar expression that conveys a similar message, i.e. novelty, as far as one can tell from the literature.

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AFAIK is used for that purpose quite frequently (: – jwpat7 Apr 25 '12 at 23:31
up vote 4 down vote accepted

When you say "to the best of my/our knowledge," you're saying that "you think your statement is true, because it is based on what you know/believe, but you are not completely sure" [Macmillan].

So any phrase that expresses that lack of complete certainty that fits the context will do. In the context of an academic paper, you might say:

We believe that this is the first work that shows how to optimize a non-submodular function...

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What about "As far as I/we know" or "As far as I/we can tell"

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In conversation, "as far as we can tell" would be fine. I'd avoid that form in an academic paper, however. – J.R. Apr 25 '12 at 23:46
This is more of a variation, but I have heard it as "To the extent of our knowledge" – Ian Apr 26 '12 at 0:04

You may use as far as we know.

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protected by tchrist Mar 1 '15 at 18:28

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