"using the logic" is correct and usable in written English.
You could use it when you want to emphasize that you are reasoning logically or that you are taking a logical approach to a problem. For example, "Using the logic of supply and demand, the company was able to maximize profits."
Using the logic of the gateway effect, this almost 100percentt correlation proves conclusively that mothers milk should be illegal.
There he refused to return fugitive slaves to the Confederacy, using the logic that they constituted "contraband of war"—an interpretation later upheld by his government.
What Ron Weiss is describing is a study his team published last autumn showing that, by using the logic of computer circuits combined with BioBricks parts, they had built a cancer assassin cell.
Using the logic of one letter writer, I would befriend and condone the actions of all those who drink and drive because I belong to the American Automobile Association.
A court ruled for the woman, using the logic that Mr. Peng would never have assisted her had he not been responsible for the fall in the first place.
In the right situation, Mr. Lovano can become something like the Laurence Olivier of jazz -- a serious practitioner with no fear, a high-wire buddha who has found his own rhythm, clearly ecstatic to be doing what he's doing and using the logic of bebop harmony and every bit of his own physicality to shape his delivery.
Likewise, all nurses were trained during a 2-month period in using the LOGIC-Insulin software.
Certain behaviors of the studied system (for example, the NFκB oscillations) can be captured only by using the logic-derived differential equations (a method that is considerably more computationally expensive, and which involves many additional arbitrary parameters).
"Schauer is pressing people to think about the language that they use, the logic that they use," Mr. Kennedy said.
Circuit design with binary quantities, "on" and "off" representing 1 and 0 (i.e., true and false), uses the logic of Boolean algebra.
Two peoples cannot reconcile when one demands control over the other, when one refuses to treat the other as a partner in peace, when one uses the logic of power rather than the power of logic.
