Formal Concept Analysis (FCA) can be used to analyze data given in the form of a formal context. In particular, FCA provides efficient algorithms for computing a minimal basis of the implications holding in the context. In this paper, we extend classical FCA by considering data that are represented by relational structures rather than formal contexts, and by replacing atomic attributes by complex formulae defined in some logic. After generalizing some of the FCA theory to this more general form of contexts, we instantiate the general framework with attributes defined in the Description Logic (DL) EL, and with relational structures over a signature of unary and binary predicates, i.e., models for EL. In this setting, an implication corresponds to a so-called general concept inclusion axiom (GCI) in EL. The main technical result of this report is that, in EL, for any finite model there is a finite set of implications (GCIs) holding in this model from which all implications (GCIs) holding in the model follow.

We present a general form of attribute exploration, a knowledge completion algorithm from formal concept analysis. The aim of this generalization is to extend the applicability of attribute exploration by a general description. Additionally, this may also allow for viewing different existing variants of attribute exploration as instances of a general form, as for example exploration on partial contexts.

Within formal concept analysis, attribute exploration is a powerful tool to semiautomatically check data for completeness with respect to a given domain. However, the classical formulation of attribute exploration does not take into account possible errors which are present in the initial data. We present in this work a generalization of attribute exploration based on the notion of confidence, which will allow for the exploration of implications which are not necessarily valid in the initial data, but instead enjoy a minimal confidence therein.

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.

We propose an approach for supporting attribute exploration by web information retrieval, in particular by posing appropriate queries to search engines, crowd sourcing systems, and the linked open data cloud. We discuss underlying general assumptions for this to work and the degree to which these can be taken for granted.

Zur einfacheren Entwicklung von technischen Systemen werden heutzutage vielfach funktionsblockorientierte Modellierungssprachen wie MATLAB/Simulink verwendet, die ein System als Netzwerk von miteinander verbundenen Funktionsblöcken darstellen. Aufgrund wechselnder Anforderungen entstehen dabei viele Modellvarianten, die nicht mehr effizient verwaltet werden können. Eine Lösung hierfür ist der Einsatz von Produktlinien, bei dem alle Varianten zusammengefasst und in wiederverwendbare Bestandteile zerlegt werden. Die Einzelvarianten werden dabei nur noch bei Bedarf aus diesen Bestandteilen zusammengesetzt. Die Erstellung dieser Produktlinien ist jedoch mit hohem manuellen Aufwand verbunden, besonders wenn vorhandene Modelle wiederverwendet werden sollen. Dies verhindert oft die Einführung dieses Paradigmas. Das Ziel der Dissertation war es deshalb, diese Migration vorhandener Modellvarianten und damit die Erstellung der Produktlinien zu automatisieren. Hierzu wurde eine Migrationsschrittfolge vorgeschlagen: Mithilfe eines Model-Matching-Ansatzes werden zuerst Gemeinsamkeiten und Unterschiede zwischen den Modellen identifiziert und daraus ein zusammengefasstes Modell und sogenannte Features abgeleitet. Mithilfe der Formalen Begriffsanalyse werden daraufhin die Abhängigkeiten zwischen diesen Features extrahiert und daraus ein Feature-Modell erstellt. Feature-Modell und zusammengefasstes Modell bilden dabei eine Produktlinie, die exakt die vorgegebenen Modellvarianten beschreibt.

Description Logics (DLs) are a class of knowledge representation formalisms that can represent terminological and assertional knowledge using a well-defined semantics. Often, knowledge engineers are experts in their own fields, but not in logics, and require assistance in the process of ontology design. This thesis presents three methods that can extract terminological knowledge from existing data and thereby assist in the design process. They are based on similar formalisms from Formal Concept Analysis (FCA), in particular the Next-Closure Algorithm and Attribute-Exploration. The first of the three methods computes terminological knowledge from the data, without any expert interaction. The two other methods use expert interaction where a human expert can confirm each terminological axiom or refute it by providing a counterexample. These two methods differ only in the way counterexamples are provided.

Zur einfacheren Entwicklung von technischen Systemen werden heutzutage vielfach funktionsblockorientierte Modellierungssprachen wie MATLAB/Simulink verwendet, die ein System als Netzwerk von miteinander verbundenen Funktionsblöcken darstellen. Aufgrund wechselnder Anforderungen entstehen dabei viele Modellvarianten, die nicht mehr effizient verwaltet werden können. Eine Lösung hierfür ist der Einsatz von Produktlinien, bei dem alle Varianten zusammengefasst und in wiederverwendbare Bestandteile zerlegt werden. Die Einzelvarianten werden dabei nur noch bei Bedarf aus diesen Bestandteilen zusammengesetzt. Die Erstellung dieser Produktlinien ist jedoch mit hohem manuellen Aufwand verbunden, besonders wenn vorhandene Modelle wiederverwendet werden sollen. Dies verhindert oft die Einführung dieses Paradigmas. Das Ziel der Dissertation war es deshalb, diese Migration vorhandener Modellvarianten und damit die Erstellung der Produktlinien zu automatisieren. Hierzu wurde eine Migrationsschrittfolge vorgeschlagen: Mithilfe eines Model-Matching-Ansatzes werden zuerst Gemeinsamkeiten und Unterschiede zwischen den Modellen identifiziert und daraus ein zusammengefasstes Modell und sogenannte Features abgeleitet. Mithilfe der Formalen Begriffsanalyse werden daraufhin die Abhängigkeiten zwischen diesen Features extrahiert und daraus ein Feature-Modell erstellt. Feature-Modell und zusammengefasstes Modell bilden dabei eine Produktlinie, die exakt die vorgegebenen Modellvarianten beschreibt.

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

Knowledge Space Theory (KST) links in several ways to Formal Concept Analysis (FCA). Recently, the probabilistic and statistical aspects of KST have been further developed by several authors. We review part of the recent results, and describe some of the open problems. The question of whether the outcomes can be useful in FCA remains to be investigated.