expressions - Analogue of "to the best of our knowledge"


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.



Answer



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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