31 January 2007, Logic Tea, Hans van Ditmarsch

This will be a presentation of joint work done with Philippe Balbiani (Institut de Recherche en Informatique de Toulouse - IRIT), Alexandru Baltag (Oxford University), Andreas Herzig (IRIT), Tomohiro Hoshi (Stanford University) and Tiago de Lima (IRIT).

Abstract:

We propose an extension of public announcement logic, called arbitrary announcement logic, with a dynamic modal operator that expresses what is true after arbitrary announcements. Intuitively, [] phi expresses that phi is true after an arbitrary announcement psi.

For an example, let us work our way upwards from a concrete announcement. When an atomic proposition p is true, it becomes known by announcing it. Formally, in public announcement logic, p & [p] K p. This is equivalent to

< p > K p

which stands for 'the announcement of p can be made and after that the agent knows p'. More abstractly this means that there is a announcement psi, namely psi = p, that makes the agent know p, slightly more formal: there is a formula psi such that < psi > K p We introduce a dynamic modal operator that expresses exactly that:

<> K p

Obviously, the truth of this expression depends on the model: p has to be true. In case p is false, we can achieve <> K ~p instead. The formula <> (K p v K ~p) is valid."

Afterwards there will be some arbitrary drinks offered at Eik and Linde.