This thesis focuses on logical formalisms to specify, design and develop self-organising and self-adaptive systems. In particular we introduce new formal languages and platforms based on non-classical logics that are able to formalise system behaviours in a rigorous way; moreover, such specifications can be directly executed in our platform, intensively reducing the gap between specification and implementation. As a result, it possible to reduce effort, time and costs of the engineering process of self-organising and self-adaptive systems. Our major contributions include: (i) a coordination model that realises the notion of coordination in terms of combinations of logic programs; (ii) a logic language based on a extendible family of many-valued logics used to perform graded paraconsistent reasoning; (iii) a logic spatial language for run-time evaluation of graph-based spatial properties in distributed systems and (iv) the implementation of the coordination model and the logic languages to implement and execute logic-based applications in heterogeneous distributed systems such as laptops, tablets and embedded devices.