We study a framework for the specification of architecture styles as families of architectures involving a common set of types of components and coordination mechanisms. The framework combines two logics: 1)~interaction logics for the specification of architectures as generic coordination schemes involving a configuration of interactions between typed components; and 2)~configuration logics for the specification of architecture styles as sets of interaction configurations. Configuration logics can be considered as a power-set extension of interaction logics. The relation between the two logics is similar to the relation between programs and their specifications. As program specifications can be expressed, \eg in temporal logics, architecture styles can be specified in configuration logics. The presented results build on previous work on architecture modelling in BIP. We show how propositional interaction logic can be extended into a corresponding configuration logic by adding new operators on sets of interaction configurations. In addition to the usual set-theoretic operators, configuration logic is equipped with a coalescing operator + to express combination of configuration sets. This operator proves to be particularly useful for the specification of architecture styles including a given class of configurations. We provide a complete axiomatization of propositional configuration logic as well as decision procedures for checking that an architecture satisfies given logical specifications. To allow genericity of specifications, we study first-order and second-order extensions of the propositional configuration logic. First-order logic formulas involve quantification over component variables. Second-order logic formulas involve additional quantification over sets of components. We provide several examples illustrating the application of the results to the characterisation of various architecture styles. We also provide an experimental evaluation using the Maude rewriting system to implement the decision procedure for the propositional flavour of the logic. We conclude with a discussion of the related work and of future directions dealing with the application of the results through the development of specific methods and tools.