General:
* Systematize: To arrange according to a system or method.
* Organize: To put in order or arrange methodically.
* Rationalize: To make rational or logical.
* Categorize: To arrange into categories.
* Structure: To give a particular form or organization to.
More specific:
* Classify: To arrange in classes or categories.
* Prioritize: To arrange in order of importance.
* Sequence: To arrange in a particular order.
* Synthesize: To combine parts into a whole, often in a logical way.
* Deduce: To reach a conclusion by reasoning.
Informal:
* Sort out: To arrange things into groups or categories.
* Figure out: To understand or solve a problem, often by arranging information logically.
The best word to use depends on the specific context and the type of logical arrangement being described.