Goal modeling is crucial in many disciplines, in particular in requirements engineering. In our work, we apply a linguistic approach, namely the theory of functional grammar, to goal authoring and discovery in requirements engineering. We represent a goal as a verb followed by parameters, each parameter having a semantic function. Since our original publication fifteen years ago, our approach has been applied in several different contexts. Capitalizing on this experience, we propose improvements and extensions to the approach. We extend the original set of semantic functions and distinguish between different levels of goal parameters. We also propose a complete syntax for formalizing goals inside parameters. Finally, we apply the extensions and the new formalization to goal authoring and discovery.