Some Sahlqvist Completeness Results for Coalgebraic Logics

Fredrik Dahlqvist; Dirk Pattinson

doi:10.1007/978-3-642-37075-5_13

Some Sahlqvist Completeness Results for Coalgebraic Logics

Fredrik Dahlqvist, Dirk Pattinson

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

Abstract / Description of output

This paper presents a first step towards completeness-via-canonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ω-accessible endofunctors and logics defined by Sahlqvist-like frame conditions. Our strategy is based on conjoining two well-known approaches: we represent accessible functors as (equational) quotients of polynomial functors and then use canonicity results for boolean algebras with operators to transport completeness to the coalgebraic setting.

Original language	English
Title of host publication	Foundations of Software Science and Computation Structures
Subtitle of host publication	16th International Conference, FOSSACS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings
Publisher	Springer
Pages	193-208
Number of pages	16
Volume	7794
ISBN (Electronic)	978-3-642-37075-5
ISBN (Print)	978-3-642-37074-8
DOIs	https://doi.org/10.1007/978-3-642-37075-5_13
Publication status	Published - 2013

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Dahlqvist Pattinson 2013 Some Sahlqvist Completeness Results for Coalgebraic LogicsAccepted author manuscript, 344 KB

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Dahlqvist, F., & Pattinson, D. (2013). Some Sahlqvist Completeness Results for Coalgebraic Logics. In Foundations of Software Science and Computation Structures: 16th International Conference, FOSSACS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings (Vol. 7794, pp. 193-208). Springer. https://doi.org/10.1007/978-3-642-37075-5_13

Dahlqvist, Fredrik ; Pattinson, Dirk. / Some Sahlqvist Completeness Results for Coalgebraic Logics. Foundations of Software Science and Computation Structures: 16th International Conference, FOSSACS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings. Vol. 7794 Springer, 2013. pp. 193-208

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title = "Some Sahlqvist Completeness Results for Coalgebraic Logics",

abstract = "This paper presents a first step towards completeness-via-canonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ω-accessible endofunctors and logics defined by Sahlqvist-like frame conditions. Our strategy is based on conjoining two well-known approaches: we represent accessible functors as (equational) quotients of polynomial functors and then use canonicity results for boolean algebras with operators to transport completeness to the coalgebraic setting.",

author = "Fredrik Dahlqvist and Dirk Pattinson",

year = "2013",

doi = "10.1007/978-3-642-37075-5_13",

language = "English",

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booktitle = "Foundations of Software Science and Computation Structures",

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Dahlqvist, F & Pattinson, D 2013, Some Sahlqvist Completeness Results for Coalgebraic Logics. in Foundations of Software Science and Computation Structures: 16th International Conference, FOSSACS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings. vol. 7794, Springer, pp. 193-208. https://doi.org/10.1007/978-3-642-37075-5_13

Some Sahlqvist Completeness Results for Coalgebraic Logics. / Dahlqvist, Fredrik; Pattinson, Dirk.
Foundations of Software Science and Computation Structures: 16th International Conference, FOSSACS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings. Vol. 7794 Springer, 2013. p. 193-208.

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

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N2 - This paper presents a first step towards completeness-via-canonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ω-accessible endofunctors and logics defined by Sahlqvist-like frame conditions. Our strategy is based on conjoining two well-known approaches: we represent accessible functors as (equational) quotients of polynomial functors and then use canonicity results for boolean algebras with operators to transport completeness to the coalgebraic setting.

AB - This paper presents a first step towards completeness-via-canonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ω-accessible endofunctors and logics defined by Sahlqvist-like frame conditions. Our strategy is based on conjoining two well-known approaches: we represent accessible functors as (equational) quotients of polynomial functors and then use canonicity results for boolean algebras with operators to transport completeness to the coalgebraic setting.

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BT - Foundations of Software Science and Computation Structures

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Dahlqvist F, Pattinson D. Some Sahlqvist Completeness Results for Coalgebraic Logics. In Foundations of Software Science and Computation Structures: 16th International Conference, FOSSACS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings. Vol. 7794. Springer. 2013. p. 193-208 doi: 10.1007/978-3-642-37075-5_13

Some Sahlqvist Completeness Results for Coalgebraic Logics

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