A categorical approach to coalgebraic fixpoint logic

Ezra Schoen; Clemens Kupke; Jurriaan Rot; Ruben Turkenburg

doi:10.1007/978-3-031-66438-0_2

A categorical approach to coalgebraic fixpoint logic

Ezra Schoen^*, Clemens Kupke, Jurriaan Rot, Ruben Turkenburg

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

Abstract

We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an initial algebra semantics, and prove they are equivalent. We also show how to place the alternation-free coalgebraic μ-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality.

Original language	English
Title of host publication	Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings
Editors	Barbara König, Henning Urbat
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	23-43
Number of pages	21
ISBN (Print)	9783031664373
DOIs	https://doi.org/10.1007/978-3-031-66438-0_2
Publication status	Published - Aug 2024
Event	17th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2024 - Luxembourg City, Luxembourg Duration: 6 Apr 2024 → 7 Apr 2024

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14617 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2024
Country/Territory	Luxembourg
City	Luxembourg City
Period	6/04/24 → 7/04/24

Funding

This research is partially supported by the Leverhulme Trust Research Project Grant RPG-2020-232 and NWO grant No. OCENW.M20.053

Keywords

fixpoint logics

Access to Document

10.1007/978-3-031-66438-0_2

Cite this

Schoen, E., Kupke, C., Rot, J., & Turkenburg, R. (2024). A categorical approach to coalgebraic fixpoint logic. In B. König, & H. Urbat (Eds.), Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings (pp. 23-43). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14617 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-66438-0_2

Schoen, Ezra ; Kupke, Clemens ; Rot, Jurriaan et al. / A categorical approach to coalgebraic fixpoint logic. Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings. editor / Barbara König ; Henning Urbat. Springer Science and Business Media Deutschland GmbH, 2024. pp. 23-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A categorical approach to coalgebraic fixpoint logic",

abstract = "We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an initial algebra semantics, and prove they are equivalent. We also show how to place the alternation-free coalgebraic μ-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality.",

keywords = "fixpoint logics",

author = "Ezra Schoen and Clemens Kupke and Jurriaan Rot and Ruben Turkenburg",

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doi = "10.1007/978-3-031-66438-0_2",

language = "English",

isbn = "9783031664373",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "23--43",

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booktitle = "Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings",

address = "Germany",

note = "17th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2024 ; Conference date: 06-04-2024 Through 07-04-2024",

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Schoen, E , Kupke, C, Rot, J & Turkenburg, R 2024, A categorical approach to coalgebraic fixpoint logic. in B König & H Urbat (eds), Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14617 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 23-43, 17th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2024, Luxembourg City, Luxembourg, 6/04/24. https://doi.org/10.1007/978-3-031-66438-0_2

A categorical approach to coalgebraic fixpoint logic. / Schoen, Ezra ; Kupke, Clemens; Rot, Jurriaan et al.
Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings. ed. / Barbara König; Henning Urbat. Springer Science and Business Media Deutschland GmbH, 2024. p. 23-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14617 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - A categorical approach to coalgebraic fixpoint logic

AU - Schoen, Ezra

AU - Kupke, Clemens

AU - Rot, Jurriaan

AU - Turkenburg, Ruben

PY - 2024/8

Y1 - 2024/8

N2 - We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an initial algebra semantics, and prove they are equivalent. We also show how to place the alternation-free coalgebraic μ-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality.

AB - We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an initial algebra semantics, and prove they are equivalent. We also show how to place the alternation-free coalgebraic μ-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality.

KW - fixpoint logics

UR - https://arxiv.org/abs/2404.16588

U2 - 10.1007/978-3-031-66438-0_2

DO - 10.1007/978-3-031-66438-0_2

M3 - Conference contribution book

AN - SCOPUS:85200676783

SN - 9783031664373

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 23

EP - 43

BT - Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings

A2 - König, Barbara

A2 - Urbat, Henning

PB - Springer Science and Business Media Deutschland GmbH

T2 - 17th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2024

Y2 - 6 April 2024 through 7 April 2024

ER -

Schoen E , Kupke C, Rot J, Turkenburg R. A categorical approach to coalgebraic fixpoint logic. In König B, Urbat H, editors, Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Proceedings. Springer Science and Business Media Deutschland GmbH. 2024. p. 23-43. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2024 Jul 26. doi: 10.1007/978-3-031-66438-0_2