16 October 2003, Logic Tea, Darko Sarenac, Stanford

Abstract: We present topological interpretation of modal logic S4 with particular emphasis on its modern use in the theory of spatial reasoning. This interpretation dates back to at least as far as a paper of J.C.C. McKinsey and A. Tarski in the 40's [The algebra of topology, Ann. of Math. (2) 45 (1944), 141--191], but until recently not much active research has been done on the topic. Recent years have seen the revival of research with applications in robotics, AI, and spatial reasoning. In the first part of the lecture, I will introduce the topological interpretation and some of its most interesting properties. If time permits, in the second part I will say something about possible extensions of this approach and some of its uses.

Prerequisites: Some knowledge of modal logic is assumed, but no (or very little) knowledge of topology.

The Logic Tea homepage can be found at https://www.illc.uva.nl/logic_tea/. For more information, please contact Merlijn Sevenster (sevenstr at science.uva.nl) or Hartmut Fitz (hfitz at hum.uva.nl).