This paper is concerned with the question of quantifying gradient degrees of acceptability by introducing the notion of Density in the context of constructional constraint language processing. We first present here our framework for language processing, where all linguistic knowledge is represented by means of constraints. The grammar itself is a constraint system. A constraint is a relation among categories, which encodes a linguistic property. But in contrast to more traditional constraint-based approaches, a constraint can hold and be assessed independently from the structure. In this context, we then introduce the notion of density, based on proportions of satisfied and violated linguistic properties. Our intuition is that density can be used as a means to measure fuzzy notions such as syntactic complexity or as a criterion to identify gradient levels of acceptability. We present and discuss early experimental results concerning density.