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On the origins of Bisimulation, Coinduction, and Fixed Points

Davide Sangiorgi, On the origins of Bisimulation, Coinduction, and Fixed Points.

The origins of bisimulation and bisimilarity are examined, in the three fields where they have been independently discovered: Computer Science, Philosophical Logic (precisely, Modal Logic), Set Theory.

Bisimulation and bisimilarity are coinductive notions, and as such are intimately related to fixed points, in particular greatest fixed points. Therefore also the appearance of coinduction and fixed points are discussed, though in this case only within Computer Science. The paper ends with some historical remarks on the main fixed-point theorems (such as Knaster-Tarski) that underpin the fixed-point theory presented.

There is a wealth of interesting information in this paper. Alas, it is not very easy to read, and the exposition can be improved. So this is not for beginners or outsiders, but if you are familiar with the topic the historical discussion will be of interest.