What's the noun for logicality? Here's the word you're looking for.
logic
(uncountable) A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method.
(philosophy) The study of the principles and criteria of valid inference and demonstration.
(mathematics) The mathematical study of relationships between rigorously defined concepts and of Mathematical_proof of statements.
“The principles of logick and natural reason tell us, that there must be a just proportion and adequation between the medium by which we prove, and the conclusion to be proved.”