Software requirements, especially non-functional requirements, are considered as vital prerequisites for producing software of high quality. As widely accepted, non-functional goal modeling like the NFR Framework usually employs tree modeling style, and presents an interactive process for the analysis of nonfunctional requirements. However, there still exist some problems during the identification of satisficing status. This paper based on the popular NFR goal model reasoning manners, clearly distinguishes the closed world assumption and the open world assumption, and proposes an automatic reasoning mechanism for NFR goal models in order to identify the satisficing statuses of the goal tree roots according to leaves’ contributions. Under a specific assumption, goals’ satisficing statuses will be transformed to affect satisficing statuses of their parents. Then parents satisficing statuses will be inferred according to the reasoning rules derived from different decomposition relationships. By alternately adopting these two steps, goal tree root’s satisficing status can be identified layer by layer. An illustrative example is used to show how our proposed formal approach works. 