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Coalgebraic logic for stochastic right coalgebras
- Source :
-
Annals of Pure & Applied Logic . Jun2009, Vol. 159 Issue 3, p268-284. 17p. - Publication Year :
- 2009
-
Abstract
- Abstract: We generalize stochastic Kripke models and Markov transition systems to stochastic right coalgebras. These are coalgebras for a functor with as an endofunctor on the category of analytic spaces, and is the subprobability functor. The modal operators are generalized through predicate liftings which are set-valued natural transformations involving the functor. Two states are equivalent iff they cannot be separated by a formula. This equivalence relation is used to construct a cospan for logical equivalent coalgebras under a separation condition for the set of predicate liftings. Consequently, behavioral and logical equivalence are really the same. From the cospan we construct a span. The central argument is a selection argument giving us the dynamics of a mediating coalgebra from the domains of the cospan. This construction is used to establish that behavioral equivalent coalgebras are bisimilar, yielding the equivalence of all three characterizations of a coalgebra’s behavior as in the case of Kripke models or Markov transition systems. [Copyright &y& Elsevier]
- Subjects :
- *SET theory
*ALGEBRAIC logic
*RELATION algebras
*ANALYTIC functions
Subjects
Details
- Language :
- English
- ISSN :
- 01680072
- Volume :
- 159
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Annals of Pure & Applied Logic
- Publication Type :
- Academic Journal
- Accession number :
- 38802654
- Full Text :
- https://doi.org/10.1016/j.apal.2008.06.018