Stochastic Relations: Congruences, Bisimulations and the Hennessy--Milner Theorem

Doberkat, Ernst–Erich

doi:10.1137/s009753970444346x

Cited by 27 publications

(50 citation statements)

References 19 publications

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“…There has been recent interest [ED06] in modal logic for systems associated with the subcategory of Meas comprising the analytic spaces, those that are continuous images of Polish spaces. The functor ∆ is replaced by the subprobability functor S, where SX is the space of measures on X having µ(X) 1.…”

Section: Conclusion and Further Questionsmentioning

confidence: 99%

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: Conclusion and Further Questionsmentioning

confidence: 99%

Deduction Systems for Coalgebras Over Measurable Spaces

Goldblatt

2008

Journal of Logic and Computation

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“…While usually computational aspects appear as the foremost concern in these investigations, it becomes evident both from [3] and from the present work that structural properties need to be looked at for their own interest, and from the understanding gained there a deeper understanding of the applications arises [2,4,5]. It may be helpful to continue with this programme from both points of view.…”

Section: Resultsmentioning

confidence: 81%

“…Smooth relations are a helpful tool for the theory of Borel sets [8], for the theory of stochastic relations [5], and, indirectly, for the theory of labelled Markov transition systems [2,4].…”

Section: Definition 1 An Equivalence Relationmentioning

confidence: 99%

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Congruences and Bisimulations for Continuous-Time Stochastic Logic

Doberkat

2005

Theoretical Aspects of Computing – ICTAC 2005

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Abstract. Continuous stochastic logic (CSL) deals with the verification of systems operating in continuous time, it may be traced to the well known tree logic CTL. We propose a probabilistic interpretation of this logic that is based on stochastic relations without making specific assumptions on the underlying distribution, and study the problem of bisimulations in a fairly general context from the viewpoint of congruences for stochastic relations. The goal is finding minimal sets of formulas that permit efficient checking of models.

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“…Investigating equivalent behavior of stochastic Kripke models for modal logics or their close cousins like the tree logics used for model checking usually follows this pattern: the state space is partitioned into states that satisfy exactly the same formulas, the existence of a bisimulation, behavioral equivalence or identification of a minimal set of formulas to test against then follows from an investigation of this equivalence relation, exploiting characteristic properties that are handed down from the logic, see [18,1,6,24,9,10]. A stochastic Kripke model is usually based on a coalgebra, and the analysis of the behavior may usually be reduced to an investigation of congruence properties for this coalgebra.…”

Section: Introductionmentioning

confidence: 99%

Stochastic coalgebraic logic: Bisimilarity and behavioral equivalence

Doberkat

2008

Annals of Pure and Applied Logic

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Bisimulations, behavioral equivalence and logical equivalence are investigated for stochastic T-coalgebras that interpret coalgebraic logic which is defined in terms of predicate liftings. We investigate the conditions for the functor under which these notions of equivalence are related by discussing congruences for the underlying stochastic relation. It is demonstrated that logics as diverse as continuous time stochastic logic and general modal logics can be usefully approached through coalgebraic methods.

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Stochastic Relations: Congruences, Bisimulations and the Hennessy--Milner Theorem

Cited by 27 publications

References 19 publications

Deduction Systems for Coalgebras Over Measurable Spaces

Deduction Systems for Coalgebras Over Measurable Spaces

Congruences and Bisimulations for Continuous-Time Stochastic Logic

Stochastic coalgebraic logic: Bisimilarity and behavioral equivalence

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