Algebraic Engineering in AI and Constructive Biology

1-5 February 1999

Faculty of Science

University of Lisbon

Portugal

Chrystopher Nehaniv

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.

For more information contact Prof. Dr. Jorge-Nuno Silva