Completeness for coalgebraic fixpoint logic
(2016) 25th EACSL Annual Conference on Computer Science Logic, CSL 2016 and the 30th Workshop on Computer Science Logic In Leibniz International Proceedings in Informatics (LIPIcs) 62. p.1-7- Abstract
We introduce an axiomatization for the coalgebraic fixed point logic which was introduced by Venema as a generalization, based on Moss' coalgebraic modality, of the well-known modal mucalculus. Our axiomatization can be seen as a generalization of Kozen's proof system for the modal mu-calculus to the coalgebraic level of generality. It consists of a complete axiomatization for Moss' modality, extended with Kozen's axiom and rule for the fixpoint operators. Our main result is a completeness theorem stating that, for functors that preserve weak pullbacks and restrict to finite sets, our axiomatization is sound and complete for the standard interpretation of the language in coalgebraic models. Our proof is based on automata-theoretic... (More)
We introduce an axiomatization for the coalgebraic fixed point logic which was introduced by Venema as a generalization, based on Moss' coalgebraic modality, of the well-known modal mucalculus. Our axiomatization can be seen as a generalization of Kozen's proof system for the modal mu-calculus to the coalgebraic level of generality. It consists of a complete axiomatization for Moss' modality, extended with Kozen's axiom and rule for the fixpoint operators. Our main result is a completeness theorem stating that, for functors that preserve weak pullbacks and restrict to finite sets, our axiomatization is sound and complete for the standard interpretation of the language in coalgebraic models. Our proof is based on automata-theoretic ideas: in particular, we introduce the notion of consequence game for modal automata, which plays a crucial role in the proof of our main result. The result generalizes the celebrated Kozen-Walukiewicz completeness theorem for the modal mu-calculus, and our automata-theoretic methods simplify parts of Walukiewicz' proof.
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- author
- Enqvist, Sebastian LU ; Seifan, Fatemeh and Venema, Yde
- organization
- publishing date
- 2016-08-01
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Automata, Coalgebra, Coalgebraic modal logic, Completeness, μ-calculus
- host publication
- 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)
- series title
- Leibniz International Proceedings in Informatics (LIPIcs)
- volume
- 62
- pages
- 7 pages
- publisher
- Schloss Dagstuhl - Leibniz-Zentrum für Informatik
- conference name
- 25th EACSL Annual Conference on Computer Science Logic, CSL 2016 and the 30th Workshop on Computer Science Logic
- conference location
- Marseille, France
- conference dates
- 2016-08-29 - 2016-09-01
- external identifiers
-
- scopus:85012898718
- ISSN
- 1868-8969
- ISBN
- 9783959770224
- DOI
- 10.4230/LIPIcs.CSL.2016.7
- language
- English
- LU publication?
- yes
- id
- e478b4ac-64e7-4936-9c76-c855182f7adb
- date added to LUP
- 2017-03-02 08:32:54
- date last changed
- 2025-04-04 14:58:22
@inproceedings{e478b4ac-64e7-4936-9c76-c855182f7adb,
abstract = {{<p>We introduce an axiomatization for the coalgebraic fixed point logic which was introduced by Venema as a generalization, based on Moss' coalgebraic modality, of the well-known modal mucalculus. Our axiomatization can be seen as a generalization of Kozen's proof system for the modal mu-calculus to the coalgebraic level of generality. It consists of a complete axiomatization for Moss' modality, extended with Kozen's axiom and rule for the fixpoint operators. Our main result is a completeness theorem stating that, for functors that preserve weak pullbacks and restrict to finite sets, our axiomatization is sound and complete for the standard interpretation of the language in coalgebraic models. Our proof is based on automata-theoretic ideas: in particular, we introduce the notion of consequence game for modal automata, which plays a crucial role in the proof of our main result. The result generalizes the celebrated Kozen-Walukiewicz completeness theorem for the modal mu-calculus, and our automata-theoretic methods simplify parts of Walukiewicz' proof.</p>}},
author = {{Enqvist, Sebastian and Seifan, Fatemeh and Venema, Yde}},
booktitle = {{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)}},
isbn = {{9783959770224}},
issn = {{1868-8969}},
keywords = {{Automata; Coalgebra; Coalgebraic modal logic; Completeness; μ-calculus}},
language = {{eng}},
month = {{08}},
pages = {{1--7}},
publisher = {{Schloss Dagstuhl - Leibniz-Zentrum für Informatik}},
series = {{Leibniz International Proceedings in Informatics (LIPIcs)}},
title = {{Completeness for coalgebraic fixpoint logic}},
url = {{http://dx.doi.org/10.4230/LIPIcs.CSL.2016.7}},
doi = {{10.4230/LIPIcs.CSL.2016.7}},
volume = {{62}},
year = {{2016}},
}