A special session on non-classical mathematics (organized by Libor Behounek and Petr Cintula) was held at the World Congress on Universal Logic (Lisbon, 22-25 April 2010). Due to a volcanic activity, only 5 out of 10 papers could be presented. See the Book of Abstracts at the congress website for the abstracts of both presented and cancelled talks. See the NCM session page at the congress website for the CFP and the list of talks.