A coalgebraic perspective on monotone modal logic

Helle Hvid Hansen; Clemens Kupke

doi:10.1016/j.entcs.2004.02.028

A coalgebraic perspective on monotone modal logic

Helle Hvid Hansen^*
, Clemens Kupke

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

56 Citations (Scopus)

Abstract

The paper has two main parts: First we make the connection between monotone modal logic and the general theory of coalgebras precise by defining functors UpP : Set → Set and UpV : Stone → Stone such that UpP- and UpV-coalgebras correspond to monotone neighbourhood frames and descriptive general monotone frames, respectively. Then we investigate the relationship between the coalgcbraic notions of equivalence and monotone bisimulation. In particular, we show that the UpP-functor does not preserve weak pullbacks, and we prove interpolation for a number of monotone modal logics using results on UpP-bisimulations.

Original language	English
Title of host publication	Proceedings of the Workshop on Coalgebraic Methods in Computer Science (CMCS 2004)
Editors	Jiri Adámek, Stefan Milius
Publisher	Elsevier
Pages	121-143
Number of pages	23
Volume	106
DOIs	https://doi.org/10.1016/j.entcs.2004.02.028
Publication status	Published - 12-Dec-2004
Externally published	Yes

Publication series

Name	Electronic Notes in Theoretical Computer Science
Publisher	Springer
Volume	106
ISSN (Print)	1571-0661

Keywords

Bisimulation
Coalgebra
Frame
Modal logic

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10.1016/j.entcs.2004.02.028Licence: CC BY-NC-ND

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title = "A coalgebraic perspective on monotone modal logic",

abstract = "The paper has two main parts: First we make the connection between monotone modal logic and the general theory of coalgebras precise by defining functors UpP : Set → Set and UpV : Stone → Stone such that UpP- and UpV-coalgebras correspond to monotone neighbourhood frames and descriptive general monotone frames, respectively. Then we investigate the relationship between the coalgcbraic notions of equivalence and monotone bisimulation. In particular, we show that the UpP-functor does not preserve weak pullbacks, and we prove interpolation for a number of monotone modal logics using results on UpP-bisimulations.",

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A coalgebraic perspective on monotone modal logic. / Hansen, Helle Hvid; Kupke, Clemens.
Proceedings of the Workshop on Coalgebraic Methods in Computer Science (CMCS 2004). ed. / Jiri Adámek; Stefan Milius. Vol. 106 Elsevier, 2004. p. 121-143 (Electronic Notes in Theoretical Computer Science; Vol. 106).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

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AU - Kupke, Clemens

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N2 - The paper has two main parts: First we make the connection between monotone modal logic and the general theory of coalgebras precise by defining functors UpP : Set → Set and UpV : Stone → Stone such that UpP- and UpV-coalgebras correspond to monotone neighbourhood frames and descriptive general monotone frames, respectively. Then we investigate the relationship between the coalgcbraic notions of equivalence and monotone bisimulation. In particular, we show that the UpP-functor does not preserve weak pullbacks, and we prove interpolation for a number of monotone modal logics using results on UpP-bisimulations.

AB - The paper has two main parts: First we make the connection between monotone modal logic and the general theory of coalgebras precise by defining functors UpP : Set → Set and UpV : Stone → Stone such that UpP- and UpV-coalgebras correspond to monotone neighbourhood frames and descriptive general monotone frames, respectively. Then we investigate the relationship between the coalgcbraic notions of equivalence and monotone bisimulation. In particular, we show that the UpP-functor does not preserve weak pullbacks, and we prove interpolation for a number of monotone modal logics using results on UpP-bisimulations.

KW - Bisimulation

KW - Coalgebra

KW - Frame

KW - Modal logic

UR - https://www.scopus.com/pages/publications/17444427759

U2 - 10.1016/j.entcs.2004.02.028

DO - 10.1016/j.entcs.2004.02.028

M3 - Conference contribution

AN - SCOPUS:17444427759

VL - 106

T3 - Electronic Notes in Theoretical Computer Science

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BT - Proceedings of the Workshop on Coalgebraic Methods in Computer Science (CMCS 2004)

A2 - Adámek, Jiri

A2 - Milius, Stefan

PB - Elsevier

ER -

A coalgebraic perspective on monotone modal logic

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