Analysing Spatial Properties on Neighbourhood Spaces

8^th June 2020, 15:00
Sven Linker
University of Liverpool

Abstract

The logic SLCS (Spatial Logic on Closure Spaces) is a modal
logic, which is defined with a generalisation of topological spaces as
its semantics. These spaces, which we will call "neighbourhood spaces"
comprise, e.g., all topological spaces. Additionally, graphs can also be
treated as neighbourhood spaces. While a model checking algorithm for
SLCS exists, the theory of the logic itself has only been studied
superficially.

In this talk, I present first results towards a model theory of SLCS. To
that end, I define a bisimulations on neighbourhood spaces, preserving
all operators of SLCS. This allows us to explore the expressiveness of
SLCS. Furthermore, I compare this bisimulation with the standard
definition of modal and converse bisimulations on graphical models.

The results are joint work with Fabio Papacchini and Michele Sevegnani.