With each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski's axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable equational theory. In our proof we develop and use a connection between projective geometries and diagonal-free cylindric algebras.

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In this paper an agent-based ambient system is presented to support persons in learning specific movement patterns. The ambient system serves as a personal coach that observes a person's movement pattern, and analyses this based on comparison with an ideal pattern generated by optimisation using a computational musculoskeletal model for this type of pattern minimizing knee joint loading. Based on this analysis the Personal Coach generates advices to adapt the person's pattern in order to better approximate the ideal pattern. The Personal Coach has been designed using the agent design method DESIRE, thereby reusing an available generic agent model. The system was evaluated (a proof of principle) by setting up an environment in which sensoring of body part positions was incorporated. In evaluations with a few subjects substantial improvement of the movement pattern compared to the ideal movement pattern was achieved.