Q: Any logic processed by a computer can be considered as Weak AI?
A: No. "Computer science defines AI research as the study of 'smart agents': any device that perceives its environment and performs actions that maximize its chance of achieving its goals successfully." - Wikipedia
Thus, it is easy to see that within this definition, common algorithms cannot be considered AI, since one or several of the elements that compose it are missing: Perception; Actuability; Objectives and -- understood in "maximize your chance to achieve your goals successfully", an adequacy function (fitness Function).
However, it is important to note that in some definitions, terms such as "learning", "taking decion", "interpreting data" and "cognition"-- for example, are extremely poorly employed and much is not even fully understood in humans, while others don’t even make sense. A good starting point is Consciousness: An Introduction
Susan Blackmore’s. You think so =]