Public Announcement under Sheaves

The goal of this article is to bring together the frameworks of model-update semantics for (propositional) public-announcement logic [9] and of sheaf semantics for first-order modal logic [2,10,14], and to thereby obtain a sheaf semantics for first-order public-announcement logic. The first attempt to extend dynamic epistemic logics to the first order was made by Kooi [15], who introduced terms to refer to epistemic agents, and an extension of public-announcement logic to the first order was briefly given by Ma [18]; both of these extensions used constant domains for interpreting first-order vocabulary. (A first-order extension of dynamic logic was given in [12,13], also with constant domains.) This article pushes ahead with these extensions by employing a sheaf structure, providing a progress toward a more flexible and useful treatment of first-order notions.