| Publication type: |
Article in Proceedings |
| Author: |
Lutz Schröder, Dirk Pattinson |
| Editor: |
Wolfgang Thomas, Pascal Weil |
| Title: |
Rank-1 Modal Logics are Coalgebraic |
| Book / Collection title: |
International Symposium on Theoretical Aspects of Computer Science (STACS 07) |
| Volume: |
4393 |
| Page(s): |
573 – 585 |
| Series: |
Lecture Notes in Computer Science |
| Year published: |
2007 |
| Publisher: |
Springer |
| Abstract: |
Coalgebras provide a unifying semantic framework for a
wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and strongly complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular generic decision procedures and upper complexity bounds, become applicable to arbitrary rank 1 modal logics, without regard to
their semantic status; we thus obtain purely syntactic versions of these results. As an extended example, we apply our framework to recently defined deontic logics.
|
| Internet: |
http://dx.doi.org/10.1007/978-3-540-70918-3_49 |
| PDF Version: |
http://www.informatik.uni-bremen.de/~lschrode/papers/rank1coalg.pdf |
| Keywords: |
semantics deduction decidability complexity modal logic coalgebra |
| Note / Comment: |
Extended version available |
| Status: |
Reviewed |
| Last updated: |
20. 02. 2009 |
