The present volume is devoted to the 'Open Russian-Finnish Colloquium on Logic' (ORFIC), held at the Saint-Petersburg State University, on June 14-16, 2012. Among the participants there were such prominent Finnish logicians as Jaakko Hintikka, Ilkka Niiniluoto and Gabriel Sandu. The volume covers the most interesting results recently obtained in different areas of research in logic. The volume is of interest to everyone concerned in modern logic.