A Coalgebraic Perspective on Monotone Modal Logic

Authors:
Helle Hvid Hansen;Clemens Kupke
Affiliations:
Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, NL--1018 TV Amsterdam;Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, NL--1018 TV Amsterdam, and Centrum voor Wiskunde en Informatica, P.O. Box 94079, NL--1090 GB Amste ...
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2004

Citing 4
Cited 13

Universal coalgebra: a theory of systems

Theoretical Computer Science - Modern algebra and its applications
Modal logic

Modal logic
A Final Coalgebra Theorem

Category Theory and Computer Science
Coalgebraic modal logic: soundness, completeness and decidability of local consequence

Theoretical Computer Science

Coalgebras and their logics

ACM SIGACT News
Expressivity of coalgebraic modal logic: The limits and beyond

Theoretical Computer Science
Admissibility of Cut in Coalgebraic Logics

Electronic Notes in Theoretical Computer Science (ENTCS)
PSPACE bounds for rank-1 modal logics

ACM Transactions on Computational Logic (TOCL)
Equational Coalgebraic Logic

Electronic Notes in Theoretical Computer Science (ENTCS)
From Coalition Logic to STIT

Electronic Notes in Theoretical Computer Science (ENTCS)
Coalgebraic modal logic in COCASL

WADT'06 Proceedings of the 18th international conference on Recent trends in algebraic development techniques
Bisimulation for neighbourhood structures

CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
The goldblatt-thomason theorem for coalgebras

CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
EXPTIME tableaux for the coalgebraic µ-calculus

CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Cut elimination in coalgebraic logics

Information and Computation
Automata for coalgebras: an approach using predicate liftings

ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Expressivity of coalgebraic modal logic: the limits and beyond

FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures

Quantified Score

Hi-index	0.00

Visualization

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 coalgebraic 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.