Coalgebraic correspondence theory (bibtex)
by Lutz Schröder, Dirk Pattinson
Abstract:
We lay the foundations of a first-order correspondence theory for coalgebraic logics that makes the transition structure explicit in the first-order modelling. In particular, we prove a coalgebraic version of the van Benthem/Rosen theorem stating that both over arbitrary structures and over finite structures, coalgebraic modal logic is precisely the bisimulation invariant fragment of first-order logic.
Reference:
Coalgebraic correspondence theory (Lutz Schröder, Dirk Pattinson), In Foundations of Software Science and Computation Structures (FoSSaCS 2010) (Luke Ong, ed.), Lecture Notes in Computer Science, vol. 6014, pp. 328–342, Springer, 2010. [preprint]
Bibtex Entry:
@InProceedings{SchroderPattinson10b,
  author = {Lutz Schr{\"o}der and Dirk Pattinson},
  title = {Coalgebraic correspondence theory},
  year = {2010},
  editor = {Luke Ong},
  booktitle = {Foundations of Software Science and Computation Structures (FoSSaCS 2010)},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  volume = {6014},
  pages = {328--342},
  keywords = {coalgebra modal logic correspondence theory rosen van benthem theorem first order logic},
  comment = { <a href = "http://www8.informatik.uni-erlangen.de/~schroeder/papers/correspondence.pdf"> [preprint] </a>},
  abstract = {  We lay the foundations of a first-order correspondence theory for
  coalgebraic logics that makes the transition structure explicit in the
  first-order modelling. In particular, we prove a coalgebraic version
  of the van Benthem/Rosen theorem stating that both over arbitrary
  structures and over finite structures, coalgebraic modal logic is
  precisely the bisimulation invariant fragment of first-order logic. 
},
}
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