Agents, attributes and observations: an overview of how (algebraic) topological models arise in CS, AI and Logic.

Photograph of Tim Porter

Tim Porter


I will briefly examine three ``case studies''.

(i) Agents: Simple models of knowledge in multiagent systems (MAS) lead to Kripke frames for the modal logic S5n and its extensions. Such models are special cases of a mathematical construct from algebraic K-theory (groupoid atlases) and these form a cartesian closed category. An analysis of runs in the MAS can be attempted via simplicial complexes associated to the frame.

(ii) Attributes (Formal Concept Analysis): A (binary) formal context consists of a set of objects and a set of attributes together with a relation between them (object x satisfies attribute y). The same simplicial complex constructions can be used here but also there are links with lattice theory and other parts of poset theory. (Possible
paradigm: agents as attributes!)

(iii) Observations: In observing a physical or a computational system, the observations can be organised by various simplicial complexes. If metric data is available then Topological Data Analysis gives geometric information on the data set. If the data set is to large, sampling leads to systems of complexes. Sorkin posets and the nerve construction will be examined.

Throughout the link between the geometry and related logics will be sketched. The central themes will include simplicial complexes posets and, above all, Chu spaces.
Tuesday 14th February 2006, 14:00
Robert Recorde Room
Department of Computer Science