The paper builds on recent results regarding the expressiveness of
modal logics for coalgebras in order to introduce a specification
framework for coalgebraic structures which offers support for modular
specification. An equational specification framework for algebraic
structures is obtained in a similar way. The two frameworks are then
integrated in order to account for structures comprising both a
coalgebraic (observational) component and an algebraic (computational)
component. The integration results in logics whose sentences are
either coalgebraic (modal) or algebraic (equational) in nature, but
whose associated notions of satisfaction take into account both the
coalgebraic and the algebraic features of the structures being
specified. Each of the logics thus obtained also supports modular
specification.
