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On Specification Logics for Algebra-Coalgebra Structures: Reconciling Reachability and Observability

C Corina

Abstract

The paper builds on recent results regarding the expressive- ness 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 struc- tures is obtained in a similar way. The two frameworks are then inte- grated 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.

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Key concepts: Coalgebra, Algebraic specification, Observability, Algebra over a field, Algebraic number, Algebraic structure, Modal, Component (thermodynamics)