The language faculty is one of the most fundamental cognitive capacities differentiating humans from other animals. Modeling language is, therefore, rightfully considered one of the main tasks of modern interdisciplinary efforts in cognitive science. Indeed, in the past decades enormous progress has been made in computational, neuro-psychological and probabilistic approaches to language. However, the centerpiece of linguistic theory needs to be a symbolic model. This is because at its very core language is a symbolic system with clear categorical regularities both within and across languages at the level of both grammatical form and meaning. Traditionally symbolic (rule-based) and probabilistic modeling of languages have been viewed as opposing scientific camps and have focused on different aspects of language such as structure vs. usage. However, in our view, progress in all relevant fields have brought about a new potential perspective on language: The core of grammar is a symbolic rule based system. But in its complex cognitive environment, the symbolic linguistic system interfaces with other cognitive components in a multitude of ways not after but preceding conventionalization of the grammar of a particular language. Thus, conventional grammar is both symbolic and probabilistic. At the same time, the tight entanglement of language and logical reasoning (currently prominently studied in the EU synergy project Leibniz Dream) also strongly affects language use and pragmatic interpretation. Hence, in our view, the key questions cognitive science needs to address in the 21st century concerns the limits and interactions between the fundamentally rule based formal linguistic system (core grammar) and the probabilistic layers that are also reflected in both language structure and use. The proposed SFB targets this very question by studying the interface between deterministic grammatical mechanisms and its probabilistic cognitive environment from a radically innovative perspective on a clearly defined empirical domain.