Gaelle will start by a survey on mu-calculus. Next she will present two little research topics. The first one is ongoing work with Yde Venema and concerns the syntactic characterization of some fragments of the mu-calculus (which are semantically defined). The second topic is joint work with Balder ten Cate and is about expressiveness of the Godel Lob logic on finite trees (the results are obtained by combining well-known modal logic results together with expressiveness results for the mu-calculus). Finally, Johan will sketch how fixed-points arise naturally in dynamic epistemic logic:
- PDL for common knowledge,
- product closure of the mu-calculus,
- fixed-points in topological semantics for epistemic logic.
The following papers illustrate these themes in more detail, but no need to study them beforehand:
- J. van Benthem, J. van Eijck & B. Kooi, 2005, ‘Logics of Communication and Change‘, “Information and Computation” 204(11): 1620 – 1662.
- J. van Benthem & D. Ikegami, 2008, ‘Modal Fixed-Point Logic and Changing Models, in A. Avron, N. Dershowitz & A. Rabinovich, eds., “Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of his 85th Birthday”, Springer, Berlin, 146 – 165.
- J. van Benthem & D. Sarenac, 2005, ‘The Geometry of Knowledge’, in J-Y Béziau, A. Costa Leite & A. Facchini, eds., “Aspects of Universal Logic”, Centre de Recherches Sémiologiques, Université de Neuchatel, 1 – 31.
Here are the slides of Gaelle’s presentation and also two papers on which it is based: