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Modular construction of modal logics
 Concurrency Theory, CONCUR 04, volume 3170 of Lect. Notes Comput. Sci
, 2004
"... Abstract. We present a modular approach to defining logics for a wide variety of statebased systems. We use coalgebras to model the behaviour of systems, and modal logics to specify behavioural properties of systems. We show that the syntax, semantics and proof systems associated to such logics can ..."
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Cited by 25 (8 self)
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Abstract. We present a modular approach to defining logics for a wide variety of statebased systems. We use coalgebras to model the behaviour of systems, and modal logics to specify behavioural properties of systems. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular way. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems. 1
Coalgebraic Modal Logic of Finite Rank
, 2002
"... This paper studies coalgebras from the perspective of finite observations. We introduce the notion of finite step equivalence and a corresponding category with finite step equivalencepreserving morphisms. This category always has a final object, which generalises the canonical model construction fr ..."
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Cited by 17 (10 self)
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This paper studies coalgebras from the perspective of finite observations. We introduce the notion of finite step equivalence and a corresponding category with finite step equivalencepreserving morphisms. This category always has a final object, which generalises the canonical model construction from Kripke models to coalgebras. We then turn to logics whose formulae are invariant under finite step equivalence, which we call logics of rank . For these logics, we use topological methods and give a characterisation of compact logics and definable classes of models.
Stone Coalgebras
"... In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue ..."
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In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue
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"... to the power set functor on the category of sets.We prove that the socalled descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. Thisyields a duality between the category of modal algebras and that of coalgebra ..."
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to the power set functor on the category of sets.We prove that the socalled descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. Thisyields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor.Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. For each such functor T we provide an adjunction between thecategory of Tsorted Boolean algebras with operators and the category of Stone coalgebrasover T. Since the unit of this adjunction is an isomorphism, this shows that Coalg(T)op isa full reflective subcategory of
SEN
, 2003
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.