Coalgebraic Simulations and Congruences

In a recent article Gorin and Schroder [3] study \(\lambda \)-simulations of coalgebras and relate them to preservation of positive formulae. Their main results assume that \(\lambda \) is a set of monotonic predicate liftings and their proofs are set-theoretical. We give a different definition of simulation, called strong simulation, which has several advantages:

[1]  Věra Trnková,et al.  Some properties of set functors , 1969 .

[2]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[3]  J. Riguet,et al.  Relations binaires, fermetures, correspondances de Galois , 1948 .

[4]  Dirk Pattinson,et al.  Coalgebraic Hybrid Logic , 2009, FoSSaCS.

[5]  Sam Staton.  Relating Coalgebraic Notions of Bisimulation , 2009, CALCO.

[6]  Dirk Pattinson,et al.  Coalgebraic modal logic: soundness, completeness and decidability of local consequence , 2003, Theor. Comput. Sci..

[7]  Corina Cîrstea,et al.  Modal Logics are Coalgebraic , 2008, Comput. J..

[8]  Daniel Gorín,et al.  Simulations and Bisimulations for Coalgebraic Modal Logics , 2013, CALCO.

[9]  Peter Aczel,et al.  A Final Coalgebra Theorem , 1989, Category Theory and Computer Science.

[10]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[11]  Dirk Pattinson,et al.  Coalgebraic Correspondence Theory , 2010, FoSSaCS.

[12]  H. Peter Gumm,et al.  Types and coalgebraic structure , 2005 .

[13]  Andrew M. Pitts,et al.  Category Theory and Computer Science , 1987, Lecture Notes in Computer Science.

[14]  Alexander Kurz,et al.  Algebra and Coalgebra in Computer Science, Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings , 2009, CALCO.

[15]  Lutz Schröder,et al.  Expressivity of coalgebraic modal logic: The limits and beyond , 2008, Theor. Comput. Sci..