by Lutz Schröder
Abstract:
In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal logic admits a complete axiomatisation in rank 1; it also enables us to establish a generic decidability result and a first complexity bound. Examples covered by these general results include, besides standard Hennessy-Milner logic, graded modal logic and probabilistic modal logic.
Reference:
Lutz Schröder: A finite model construction for coalgebraic modal logic, In Journal of Logic and Algebraic Programming (FOSSACS 06 special issue), 73, pp. 97–110, 2007. Extends (Schröder 2006) [preprint]
Bibtex Entry:
@Article{Schroder07,
author = {Lutz Schr{\"o}der},
title = {A finite model construction for coalgebraic modal logic},
year = {2007},
journal = {Journal of Logic and Algebraic Programming (FOSSACS 06 special issue)},
volume = {73},
pages = {97-110},
keywords = {Coalgebra Modal Logic Decision Procedures Complexity Filtrations},
url = {http://dx.doi.org/10.1016/j.jlap.2006.11.004},
comment = { <a href = "http://www8.informatik.uni-erlangen.de/~schroeder/papers/CMLfmp-ext.pdf"> [preprint] </a>},
abstract = {In recent years, a tight connection has emerged between modal logic on
the one hand and coalgebras, understood as generic transition systems,
on the other hand. Here, we prove that (finitary) coalgebraic modal
logic has the finite model property. This fact not only reproves known
completeness results for coalgebraic modal logic, which we push further
by establishing that every coalgebraic modal logic admits a complete
axiomatisation in rank 1; it also enables us to establish a generic
decidability result and a first complexity bound. Examples covered by
these general results include, besides standard Hennessy-Milner logic,
graded modal logic and probabilistic modal logic.
},
note = {Extends (Schröder 2006)},
}