| Publication type: |
Article in Proceedings |
| Author: |
Dirk Pattinson, Lutz Schröder |
| Editor: |
Roberto Amadio |
| Title: |
Beyond Rank 1: Algebraic Semantics and Finite Models for Coalgebraic Logics |
| Book / Collection title: |
Foundations of Software Science and Computation Structures (FOSSACS 2008) |
| Volume: |
4962 |
| Page(s): |
66 – 80 |
| Series: |
Lecture Notes in Computer Science |
| Year published: |
2008 |
| Publisher: |
Springer |
| Abstract: |
Coalgebras provide a uniform framework for the semantics of a large
class of (mostly non-normal) modal logics, including e.g. monotone
modal logic, probabilistic and graded modal logic, and coalition
logic, as well as the usual Kripke semantics of modal logic. In
earlier work, the finite model property for coalgebraic logics has
been established w.r.t. the class of emphall structures
appropriate for a given logic at hand; the corresponding modal
logics are characterised by being axiomatised in rank 1, i.e.
without nested modalities. Here, we extend the range of coalgebraic
techniques to cover logics that impose global properties on their
models, formulated as frame conditions with possibly nested
modalities on the logical side (in generalisation of frame
conditions such as symmetry or transitivity in the context of Kripke
frames).
We show that the finite model property for such logics follows from
the finite algebra property of the associated class of complex
algebras, and then investigate sufficient conditions for the finite
algebra property to hold. Example applications include extensions
of coalition logic and logics of uncertainty and knowledge.
|
| Internet: |
http://dx.doi.org/10.1007/978-3-540-78499-9_6 |
| PDF Version: |
http://www.informatik.uni-bremen.de/~lschrode/papers/fmp-fap.pdf |
| Keywords: |
Coalgebra modal logic frame conditions algebraic semantics quantitative uncertainty coalition logic |
| Status: |
Reviewed |
| Last updated: |
18. 06. 2008 |
