Coalgebras and their logics

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Abstract
Some comments about the last Logic Column, on nominal logic. Pierre Lescanne points out that the terminology “de Bruijn levels” was introduced in the paper Explicit Substitutions with de Bruijn’s Levels, by Pierre Lescanne and Jocelyne Rouyer-Degli, presented at the 1995 RTA conference. He also points out that Stoy diagrams were probably invented by Stoy, but appear in work by Bourbaki as early as 1939 (published in 1954). Merci, Pierre. That article also initiated what is bound to be an interesting discussion. The critique of higherorder abstract syntax in that article prompted Karl Crary and Robert Harper to prepare a response to the leveled criticisms. The response should appear in an upcoming Column. In this issue, Alexander Kurz describes recent work on the topic of specifying properties of transition systems. It turns out that by giving a suitably abstract description of transition systems as coalgebras, we can derive logics for capturing properties of these transition systems in a rather elegant way. I will let you read the details below. I am always looking for contributions. If you have any suggestion concerning the content of the Logic Column, or if you would like to contribute by writing a column yourself, feel free to get in touch with me.

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