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The phrase "a second reasoning" is correct and usable in written English.
It can be used when referring to an additional or alternative line of reasoning in an argument or discussion.
Example: "After considering the first argument, I would like to present a second reasoning that supports my position."
Alternatives: "an alternative rationale" or "a different argument".
Exact(2)
A second reasoning relates to the egg-shell distribution of V, which promotes zeolite destruction by mechanisms described in the literature.
As a second reasoning can be found in the exemplary study on p. 234 [ 5]: "Measures of treatment effects such as effect sizes of the t-test statistic are in itself only useful for interpretation of score changes, not for assessing the responsiveness of a measure, because it will not be possible to infer if a corresponding change in the concept has taken place".
Similar(58)
President Obama's second reasoning is a little clearer.
Second, reasoning the other temporal relationships is also possible (R2).
A second measure of reasoning was Reasoning about Multiple Answers, in which reasons for more than one answer were considered by the group.
One potential solution would be to assign both tiers to a dimension representing "knowledge" and tier 2 to a second dimension for "reasoning".
A second line of reasoning suggests biological mechanisms could also be implicated as underlying factors.
Similar findings have been obtained for a second type of reasoning bias, namely covariation bias.
After we had completed collection of motor neurons by microdissection, we collected the remaining anterior horn region to create a second sample set, reasoning that this might be important for understanding disease pathogenesis given the strong evidence for non-autonomous degeneration in ALS (3, 4).
House leaders opted to allow the Senate to strike first, reasoning that a strong, bipartisan vote there would splinter Republican support in the House, Democratic leadership aides said.
First, reasoning services in SWRL (a combination of OWL and RuleML) are not decidable.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com