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The language faculty forms part of the cognitive system, and as such the use of language is constrained by cognitive limitations of the individual language user. At the same time, language is a tool for social interaction and communication, and as such must provide flexible but efficient mechanisms which enable the language users to achieve communicative success with a variety of interlocutors. The way people use language therefore exhibits a high degree of variability at all levels of linguistic description. At the same time, some linguistic features seem to be more stable, or robust, than others. By exploring the systematicity and the limits of variability in linguistic behaviours, the main focus of the proposed CRC will lie on identifying the constraints of the underlying linguistic system. The planned CRC characterises variability in language as the range of different possible linguistic behaviours that are available to a language user, a language community, or in specific languages at any linguistic level. The limits of variability in linguistic behaviour become evident when a linguistic behaviour is relatively consistent, that is, resistant to influences of cognitive factors, social situations, conventions, and change, and/or when it shows relative consistency across and within languages, language communities, and individuals. The limits of variability will inform us about more stable constraints of the underlying linguistic system. The CRC addresses different subtypes of variability, namely variability between and within languages, language communities, and individuals. The central assumption is that the patterns and the limits of variability in these subtypes have important properties in common, and that variability is not just reducible to random noise. We hypothesise that features that are more stable at one level of linguistic analysis may also be more stable at others. The projects in the CRC will jointly evaluate the limits, relations, dependencies, and commonalities of the different types of variability across a range of linguistic phenomena from the perspectives of (A) language interaction and change, of (B) language processing, and of (C) the grammar systems. By modelling the factors that influence linguistic behaviours across a variety of linguistic phenomena, projects in the CRC aim to get a clearer picture of the underlying mental representations and processing architectures in the individual and of the grammatical options that are inherent in a language, in a specific variety of that language, or in a particular language-contact situation, with the final goal of improving linguistic, psycho-/neurolinguistic, and computational models of language.