"logical continuation" is correct and can be used in written English, and can be used when you want to express a logical flow from one idea to the next.
For example: "The evidence clearly points to the defendant's guilt; a logical continuation of this conclusion is that they should be brought to justice."
"It is the logical continuation of a very strong supplier".
They are a logical continuation of policies to increase levels of school autonomy".
A move toward ensemble acting was perhaps the logical continuation of efforts to achieve scenic realism.
Look skeptically on commentators who claim that this music is a logical continuation of a historical line extending at least back to Mozart.
This position doesn't obviously fit with that, but read on… RB I don't know this line of the Closed Sicilian but doesn't 1…Bb7 seem the logical continuation?
For Qatari officials, their intervention in Libya is not a break but a logical continuation of an active foreign policy aimed at pushing for regional modernization.
The medieval problem of universals is a logical, and historical, continuation of the ancient problem generated by Plato's (428-348 B.C). theory answering such a bundle of questions, namely, his theory of Ideas or Forms.
But for them, this is the only logical choice because a continuation of the nuclear stand-off would only further worsen human rights conditions in Iran.
Indeed, Godknows, Enough and company are a continuation of an African tradition arguably more logical than the one that churns out Justins and Tiffanys in America.
CL was originally invented as a continuation of the reduction of the set of logical constants to a singleton in classical first-order logic (FOL).
The company sees the product as not only a logical next step in its professional music product line, but a continuation of the audio work it's invested in its amps over the years.
