The Fregean-inspired Principle of Compositionality of Meaning (PoC), for formal languages, may be construed as asserting that the meaning of a compound expression is deterministically (and often recursively) analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint --that may or may not be respected-- on the internal mechanisms that build and give meaning to a given formal system. Within the domain of formal semantics and of the structure of logical derivations, PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally well-behaved logical systems.The project GeTFun aims at being a coordinated exchange programme for the investigation of compositional meaning in logic and applications. The consortium will study various well-motivated ways in which the attractive properties and metaproperties of truth-functional logics may be stretched so as to cover more extensive logical grounds. The ubiquity of non-classical logics in the formalization of practical reasoning demands the formulation of more flexible theories of meaning and compositionality that allow for the establishment of coherent and inclusive bases for their understanding. Such investigations presuppose not only the development of adequate frameworks from the perspectives of Model Theory, Proof Theory and Universal Logic, but also the construction of solid bridges between the related approaches based on various generalizations of truth-functionality. Applications of broadly truth-functional logics, in their various guises, are envisaged in several areas of computer science, mathematics, philosophy and linguistics, where the ever increasing complexity of systems continuously raise new and difficult challenges to compositionality.