1-5 February 1999
Faculty of Science
University of Lisbon
Interactive Systems Engineering
University of Hertfordshire, U.K.
I plan three talks giving an intensive introduction to aspects of Algebraic Engineering in the areas of embodied Artificial Intelligence and applications to Natural and Constructive Biology. The work reported ranges from Krohn-Rhodes Algebraic Theory of Automata and Semigroups developed in the 1960s to some applications developed more recently in collaboration with John Rhodes and Kerstin Dautenhahn.
Lecture 1. Algebra for Formal Models Affording Understanding
We review the elementary global decomposition theory of (generally finite) semigroups. We overview some of its methods, and motivate them by giving examples showing that they can be understood as methods to derive formal models for understanding phenomena that can be modelled in automata theory. The (non-unique) models provided by these decompositions give (alternative) feedback-free coordinate systems in which to understand the systems in question. Natural examples include clocks, the decimal expansion, Lagrange coordinates on symmetry groups, and conservation laws in physics.
Lecture 2. The Evolution of Biological Complexity from an Algebraic Perspective
We discuss the oft-used and rarely defined notion of `complexity' for biological systems. We show the existence of a unique maximal complexity measure for biological systems (via a route through the algebraic theory of semigroups). Some consequences for the rate at which biological complexity may increase are derived, and these are considered in the light of major evolutionary transitions in the history of life on earth.
Lecture 3. Algebras of Time and History for Autobiographic Agents
We discuss how semigroups can be viewed as the models of (local) time for agents acting in the world. A key problem in post-reactive robotics is the historical grounding of agents as `autobiographic agents' that construct their own histories as they interact with the world. Expansions (certain functorial constructions) of semigroups are systematic ways of recording histories (which are themselves elements of an expanded algebra). These methods may have useful applications for robotic and software agents in temporal grounding, exchange of narrative histories (`story-telling'), imitation, and in social intelligence.