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On Generalised Coinduction and Probabilistic Specification Formats: Distributive Laws in Coalgebraic Modelling
, 2004
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Definability, Canonical Models, Compactness for Finitary Coalgebraic Modal Logic
, 2007
"... This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours ..."
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Cited by 5 (3 self)
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This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.
Distributivity of Categories of Coalgebras
"... We prove that for any F the category of F coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever has finite products. ..."
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Cited by 2 (2 self)
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We prove that for any F the category of F coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever has finite products.
Logical Relations for Monadic Types †
, 2004
"... Logical relations and their generalizations are a fundamental tool in proving properties of lambdacalculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi’s computational lambdacalculus. Th ..."
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Logical relations and their generalizations are a fundamental tool in proving properties of lambdacalculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi’s computational lambdacalculus. The treatment is categorical, and is based on notions of subsconing, mono factorization systems, and monad morphisms. Our approach has a number of interesting applications, including cases for lambdacalculi with nondeterminism (where being in logical relation means being bisimilar), dynamic name
Final Coalgebras And a Solution Theorem for Arbitrary Endofunctors
"... Every endofunctor F of Set has an initial algebra and a final coalgebra, but they are classes in general. Consequently, the endofunctor F ∞ of the category of classes that F induces generates a completely iterative monad T. And solutions of arbitrary guarded systems of iterative equations w.r.t. F e ..."
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Every endofunctor F of Set has an initial algebra and a final coalgebra, but they are classes in general. Consequently, the endofunctor F ∞ of the category of classes that F induces generates a completely iterative monad T. And solutions of arbitrary guarded systems of iterative equations w.r.t. F exist, and can be found in naturally defined subsets of the classes T Y.
Under consideration for publication in Math. Struct. in Comp. Science Logical Relations for Monadic Types †
, 2005
"... Logical relations and their generalizations are a fundamental tool in proving properties of lambdacalculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi’s computational lambdacalculus. Th ..."
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Logical relations and their generalizations are a fundamental tool in proving properties of lambdacalculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi’s computational lambdacalculus. The treatment is categorical, and is based on notions of subsconing, mono factorization systems, and monad morphisms. Our approach has a number of interesting applications, including cases for lambdacalculi with nondeterminism (where being in logical relation means being bisimilar), dynamic name
Comment.Math.Univ.Carolin. 46,2 (2005)197–215 197 Birkhoff’s Covariety Theorem without limitations
"... To my teacher and friend Věra Trnková, from whom I have learned so much, on the occasion of her seventieth birthday. Abstract. J. Rutten proved, for accessible endofunctors F of Set, the dual Birkhoff’s Variety Theorem: a collection of Fcoalgebras is presentable by coequations ( = subobjects of ..."
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To my teacher and friend Věra Trnková, from whom I have learned so much, on the occasion of her seventieth birthday. Abstract. J. Rutten proved, for accessible endofunctors F of Set, the dual Birkhoff’s Variety Theorem: a collection of Fcoalgebras is presentable by coequations ( = subobjects of cofree coalgebras) iff it is closed under quotients, subcoalgebras, and coproducts. This result is now proved to hold for all endofunctors F of Set provided that coequations are generalized to mean subchains of the cofreecoalgebra chain. For the concept of coequation introduced by H. Porst and the author, which is a subobject of a member of the cofreecoalgebra chain, the analogous result is false, in general. This answers negatively the open problem of A. Kurz and J. Rosicky ́ whether every covariety can be presented by equations w.r.t. cooperations.