Formal concept analysis (FCA) is a mathematical formalism based on order and lattice theory for data analysis. It has found applications in a broad range of neighboring fields including Semantic Web, data mining, knowledge representation, data visualization and software engineering. ICFCA is a series of annual international conferences that started in 2003 in Darmstadt and has been held in several continents: Europe, Australia, America and Africa. ICFCA has evolved to be the main forum for researchers working on theoretical or applied aspects of formal concept analysis worldwide. In 2013 the conference returned to Dresden where it was previously held in 2006. This year the selection of contributions was especially competitive. This volume is one of two volumes containing the papers presented at ICFCA 2013. The other volume is published by Springer Verlag as LNAI 7880 in its LNCS series. In addition to the regular contributions, we have included an extended abstract: Jean-Paul Doignon reviews recent results connecting formal concept analysis and knowledge space theory in his contribution “Identifiability in Knowledge Space Theory: a Survey of Recent Results”. The high-quality of the program of the conference was ensured by the much-appreciated work of the authors, the Program Committee members, and the Editorial Board members. Finally, we wish to thank the local organization team. They provided support to make ICFCA 2013 proceed smoothly in a pleasant atmosphere.:EXTENDED ABSTRACT Jean-Paul Doignon: Identifiability in Knowledge Space Theory: a survey of recent results S. 1 REGULAR CONTRIBUTIONS Ľubomír Antoni, Stanislav Krajči, Ondrej Krídlo and Lenka Pisková: Heterogeneous environment on examples S. 5 Robert Jäschke and Sebastian Rudolph: Attribute Exploration on the Web S. 19 Adam Krasuski and Piotr Wasilewski: The Detection of Outlying Fire Service’s Reports. The FCA Driven Analytics S. 35 Xenia Naidenova and Vladimir Parkhomenko: An Approach to Incremental Learning Based on Good Classification Tests S. 51 Alexey A. Neznanov, Dmitry A. Ilvovsky and Sergei O. Kuznetsov: FCART: A New FCA-based System for Data Analysis and Knowledge Discovery S. 65