The phrase "in line with the logic" is correct and usable in written English.
You can use it when you are referring to something that is consistent with the logic or rationale of a particular argument. For example, "The changes to the policy are in line with the logic that our customers should be treated fairly."
In line with the logic of the reforms made in 1992, the commission wants further sharp cuts in the guaranteed prices that the CAP offers to farmers for most of their products, and to make direct compensatory payments, unrelated to production, instead.
We prefer to explicitly call the ratio of the working-age to the non-working-age population the total support ratio, in line with the logic of the three versions of dependency ratio: total, youth, and old-age.
The formation of a Conservative-Liberal Democratic coalition in May 2010 was fully in line with the dominant political logic of realignment.
The research results suggest that to increase the likelihood of successfully implementing a water infrastructure project, an efficient business strategy would be to work proactively with the legislation in line with the decision-making logic indicated in the provided guidance.
In line with the prevailing conception of logic as essentially sentential, however, they are not usually thought to play a role in rigorous mathematical reasoning.
This is, for example, the path taken in Kripke (1963), where Kripke proposes to weaken the axiom of universal instantiation in line with the first version of inclusive quantificational logic discussed earlier.
"It is in line with the idea of bringing candombe rhythm logic and culture to the club.
However, at a more general level GPs' behaviour may reflect a 'logic of care' rather than a 'logic of choice' [ 41] - GPs making choices based on their professional views on patients' needs and wants, rather than as agents acting in a market place enabling patients to make informed choices in line with the neoclassical standard model.
In line with pharmacological logic, De Pascale and colleagues showed that increasing the TGC dose improved clinical outcome without enhancing toxicity.
Students will leave, funding will disappear, and the curators won't stand in line with his twisted logic.
This is in line with traditional compression logic, where high-frequency information can often be discarded without causing an exaggerated increase in distortion.
