This study takes the interaction between human beings and intelligent systems from a rather basic perspective, that of the exchanged information. Interactions with artificial intelligence (AI) systems is usually studied from the perspective of the fact that they provide information that is apt to the task at hand, that is operational in the sense that it supports the undergoing activity. The practice of the interaction is rather different in that information may result ambiguous, difficult to understand, or completely irrelevant. This paper proposes a typology of non-functional information, by classifying it in: (a) dysfunctional, that is information that is detrimental to the task at hand; (b) pseudo-functional, that is seemingly useful but its use is unclear; and (c) irrelevant information, that is of no use. These three categories are confronted with information that is perceived and is actually functional, i.e. useful for the goal it is supposed to serve. In an attempt to explore the workings of these information types, I use a systemic e-cognition (SEC) approach. This allows to change the discourse on information such that it becomes tied to the cognitive interactive system rather than objectively and neutrally defined. The proposed typology is then put to the test by using an agent-based computational simulation model (ABM) where teams gather information from tools—intended as AI systems—as to perform a task. Results show that all the three types of information are related to task performance. This is somehow surprising given that non-functional information has been traditionally discarded as non-existent to the task at hand. Instead, the simulation shows that, from an organizational or systemic perspective, even non-functionally-related interactions serve to “prepare” the tool to further interaction and eventual performance.