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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Presenting Functors by Operations and Equations
verfasst von : Marcello M. Bonsangue, Alexander Kurz
Erschienen in: Foundations of Software Science and Computation Structures
Verlag: Springer Berlin Heidelberg
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We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for T-coalgebras and investigate under which circumstances it gives rise to a ‘concrete’ such logic, that is, a logic with an inductively defined syntax and proof system. We obtain a result that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness.