Coinductive Predicates and Final Sequences in a Fibration

Hasuo, Ichiro; Cho, Kenta; Kataoka, Toshiki; Jacobs, Bart

doi:10.1016/j.entcs.2013.09.014

Cited by 14 publications

(24 citation statements)

References 22 publications

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“…As a consequence of the second part of Lemma 10.6, the lax Pre-liftings of the functors F × Id, S(F × Id) and F T with respect to the orders in (22) are respectively given by…”

Section: Monotone Gsosmentioning

confidence: 99%

“…The fibrations Rel(Nom) → Nom and Sub(Nom) → Nom are well-founded in the sense of [22]. To prove this we can apply [22,Lemma 3.4], which gives as a sufficient condition for well-foundedness: that the fibre above each finitely presentable object be finite.…”

Section: Soundness Of Bisimulation Up To Congruencementioning

confidence: 99%

“…3 we have argued that systems are modeled as coalgebras in a certain "base" category, whereas coinductive predicates and invariants are coalgebras in categories of "properties". As explained in [22,23], the basic infrastructure for modeling systems and their coinductive properties is provided in a systematic manner by fibrations, as we recall next. Given a fibration p : E → B, the idea is that the systems of interest are modeled as coalgebras for a functor F : B → B. Coinductive predicates for a coalgebra ξ : X → F X are then coalgebras themselves, for a functor on the fibre E X above X .…”

Section: Coinductive Predicatesmentioning

confidence: 99%

“…For Bhv, we note that F τ is defined exactly as in coalgebraic modal logic [17,22] and thus (F τ , F) is a fibration map: Theorem 6.1 applies. By using Proposition 3.4(i), Bhv is …”

Section: This Proves Thatmentioning

confidence: 99%

“…The final coalgebra, or greatest fixed-point for such a B is called a coinductive predicate [22,23]. Considering appropriate liftings F, one obtains, for instance, various behavioural preorders: similarity on labeled transition systems (LTSs), language inclusion on automata, or lexicographic ordering of streams.…”

Section: To (ξ × ξ) −1 (R)mentioning

confidence: 99%

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A general account of coinduction up-to

et al. 2016

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Bisimulation up-to enhances the coinductive proof method for bisimilarity, providing efficient proof techniques for checking properties of different kinds of systems. We prove the soundness of such techniques in a fibrational setting, building on the seminal work of Hermida and Jacobs. This allows us to systematically obtain up-to techniques not only for bisimilarity but for a large class of coinductive predicates modeled as coalgebras. The fact that bisimulations up to context can be safely used in any language specified by GSOS rules can also be seen as an instance of our framework, using the well-known observation by Turi and Plotkin that such languages form bialgebras. In the second part of the paper, we provide a new categorical treatment of weak bisimilarity on labeled transition systems and we prove the soundness of up-to context for weak bisimulations of systems specified by cool rule formats, as defined by Bloom to ensure congruence of weak bisimilarity. The weak transition systems obtained from such cool rules give rise to lax bialgebras, rather than to bialgebras. Hence, to reach our goal, we extend the categorical framework developed in the first part to an ordered setting. B Daniela Petrişan

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“…As a consequence of the second part of Lemma 10.6, the lax Pre-liftings of the functors F × Id, S(F × Id) and F T with respect to the orders in (22) are respectively given by…”

Section: Monotone Gsosmentioning

confidence: 99%

Section: Soundness Of Bisimulation Up To Congruencementioning

confidence: 99%

Section: Coinductive Predicatesmentioning

confidence: 99%

“…For Bhv, we note that F τ is defined exactly as in coalgebraic modal logic [17,22] and thus (F τ , F) is a fibration map: Theorem 6.1 applies. By using Proposition 3.4(i), Bhv is …”

Section: This Proves Thatmentioning

confidence: 99%

Section: To (ξ × ξ) −1 (R)mentioning

confidence: 99%

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A general account of coinduction up-to

et al. 2016

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Fibrational Bisimulations and Quantitative Reasoning

Sprunger

Katsumata

Dubut

et al. 2018

Lecture Notes in Computer Science

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Bisimulation and bisimilarity are fundamental notions in comparing state-based systems. Their extensions to a variety of systems have been actively pursued in recent years, a notable direction being quantitative extensions. In this paper we present an abstract categorical framework for such extended (bi)simulation notions. We use coalgebras as system models and fibrations for organizing predicatesfollowing the seminal work by Hermida and Jacobs-but our focus is on the structural aspect of fibrational frameworks. Specifically we use morphisms of fibrations as well as canonical liftings of functors via Kan extensions. We apply this categorical framework by deriving some known properties of the Hausdorff pseudometric and approximate bisimulation in control theory.

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Coalgebraic Methods in Computer Science

Petrişan

Rot

2020

Lecture Notes in Computer Science

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The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

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Coinductive Predicates and Final Sequences in a Fibration

Cited by 14 publications

References 22 publications

A general account of coinduction up-to

A general account of coinduction up-to

Fibrational Bisimulations and Quantitative Reasoning

Coalgebraic Methods in Computer Science

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