Final coalgebras for functors on measurable spaces

Moss, Lawrence S.; Viglizzo, Ignacio

doi:10.1016/j.ic.2005.04.006

Cited by 29 publications

(23 citation statements)

References 14 publications

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“…The notion of measurable polynomial functor was introduced and developed in [MV04,Vig05,MV06], where it is shown that the category of T -coalgebras and T -morphisms for a measurable polynomial T has a terminal object, known as a final T -coalgebra. 1…”

Section: Measurable Functors and Coalgebrasmentioning

confidence: 99%

“…The set Ing T of ingredients can be defined inductively by putting Vig05,MV06] do not discuss exponential functors, but the theory readily includes them. X E is essentially a special case of the direct product Q e∈E Xe with Xe = X.…”

Section: The Multigraph Of Ingredientsmentioning

confidence: 99%

“…A new dimension to this area has now been added by the work of Moss and Viglizzo [MV04,Vig05,MV06], replacing Set by the category Meas of measurable spaces. They study measurable polynomial functors, analogues of KPF's in which P is replaced by a functor ∆ assigning to each measurable space X a space ∆X whose points are the probability measures on X.…”

Section: Introductionmentioning

confidence: 99%

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Deduction Systems for Coalgebras Over Measurable Spaces

Goldblatt

2008

Journal of Logic and Computation

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A theory of infinitary deduction systems is developed for the modal logic of coalgebras for measurable polynomial functors on the category of measurable spaces. These functors have been shown by Moss and Viglizzo to have final coalgebras that represent certain universal type spaces in game-theoretic economics. A notable feature of the deductive machinery is an infinitary Countable Additivity Rule.A deductive construction of canonical spaces and coalgebras leads to completeness results. These give a proof-theoretic characterisation of the semantic consequence relation for the logic of any measurable polynomial functor as the least deduction system satisfying Lindenbaum's Lemma. It is also the only Lindenbaum system that is sound.The theory is additionally worked out for Kripke polynomial functors, on the category of sets, that have infinite constant sets in their formation.

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Section: Measurable Functors and Coalgebrasmentioning

confidence: 99%

Section: The Multigraph Of Ingredientsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deduction Systems for Coalgebras Over Measurable Spaces

Goldblatt

2008

Journal of Logic and Computation

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“…Moss and Viglizzo [23,30] showed that polynomial functors extended with the Giry functor have a final coalgebra. Therefore, for L a finite set of action labels, we are allowed to safely adopt behavioural equivalence over ∆ L -coalgebras, since ∆ L ∼ = α∈L ∆ is a finite product, hence admits a final coalgebra.…”

Section: Continuous Probabilistic Systems As Coalgebrasmentioning

confidence: 99%

“…However, in order to port this approach to our setting we have to solve several technical issues, due to the fact that we are working in Meas and using the Giry functor ∆. First, ∆ does not preserve weak pullbacks [23,30], hence we cannot prove that bisimilarity is transitive and that it coincides with behavioural equivalence. As a consequence, we focus on behavioural equivalence instead of bisimilarity.…”

Section: Introductionmentioning

confidence: 99%