On January 10, we will have a we will have a LIRa session with Kohei Kishida.
Everyone is cordially invited!
Speaker: Kohei Kishida (ILLC, UvA)
Title: Public Announcements under Sheaves
Date and Time: Thursday, January 10, 2013, 15:30-17:30
Venue: Science Park 904, Room A1.04
Abstract:
This paper brings together the frameworks of model-update semantics for (propositional) public-announcement logic and of sheaf semantics for first-order modal logic, and to thereby obtain a sheaf semantics for first-order public announcement logic. The first attempt to extend dynamic epistemic logic to the first order was briefly made in [2], with constant domains for interpreting first-order vocabulary. The goal of this paper is to push ahead with this extension by employing neighborhood structures and sheaf structures, providing a progress toward a more flexible and useful treatment of knowledge operators and first-order notions.
In particular, we lay out three elements of extension for the standard PAL:
(i) the (monotone) neighborhood setting (an extension first given in [1]);
(ii) the first-order version FOPAL [2]; and (iii) its neighborhood-sheaf semantics. (i) facilitates an “observability and verifiability” interpretation of knowledge operators that is not available to Kripke semantics. (ii) brings into the PAL analysis of dynamic and epistemic processes a first-order vocabulary, and in particular names for individuals. And, lastly, (iii) gives us a flexible way of modelling how a first-order ontology as well as first-order vocabulary can evolve in dynamic and epistemic processes. This work lays the foundation for modal-logical analyses of such evolution.
References:
[1] Demey, L., “Towards a Dynamics of Realistic Knowledge: Neighborhood
Semantics for Public Announcement Logic”, paper read at _Fourth Conference
of the Dutch-Flemish Association for Analytic Philosophy_, Leuven, Belgium,
on Jan. 21, 2010.
[2] Ma, M., “Mathematics of Public Announcements”, in H. van Ditmarsch, J.
Lang, and S. Ju, eds., _Logic, Rationality and Interaction: Third
International Workshop, LORI 2011_, Springer, 2011, pp. 193–205.