Coalgebras and Modal Logic (2000)
| Venue: | Coalgebraic Methods in Computer Science, Volume 33 in Electronic Notes in Theoretical Computer Science |
| Citations: | 32 - 0 self |
BibTeX
@INPROCEEDINGS{Rößiger00coalgebrasand,
author = {Martin Rößiger},
title = {Coalgebras and Modal Logic},
booktitle = {Coalgebraic Methods in Computer Science, Volume 33 in Electronic Notes in Theoretical Computer Science},
year = {2000},
pages = {299--320},
publisher = {Elsevier}
}
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Abstract
Coalgebras are of growing importance in theoretical computer science. To develop languages for them is significant for the specification and verification of systems modelled with them. Modal logic has proved to be suitable for this purpose. So far, most approaches have presented a language to describe only deterministic coalgebras. The present paper introduces a generalization that also covers non-deterministic systems. As a special case, we obtain the "usual" modal logic for Kripke-structures. Models for our modal language L F are F-coalgebras where the functor F is inductively constructed from constant sets and the identity functor using product, coproduct, exponentiation, and the power set functor. We define a language L F and show that it embeds into L F . We prove that, for image-finite coalgebras, L F is expressive enough to distinguish elements up to bisimilarity and therefore L F does so, too. Moreover, we also give a complete calculus for L F in case the constants...
