Logic-based applications often use customized logics which are composed of several logics. These customized logics are also often embedded as a black-box in an application. So, implementing them requires the specification of a well-defined interface with common operations such as a parser, a printer, and a theorem prover. In order to be able to compose these logic, one must also define composition laws, and prove their properties. We present the principles of logic functors and their compositions for constructing logics that are ad-hoc, but sound. An important issue is how the operations of different sublogics inter-operate. We propose a formalization of the logic functors, their semantics, implementations, proof-theoretic properties, and their composition.