Editorial

This special issue of the International Journal of General Systems is dedicated to applications of concept lattices.

The Concept Lattices and their Applications Conference (CLA) is an annual event that began in 2003 as a response to the increasing use of concept lattices in practical domains. In 2007, the 5th Concept Lattices and their Applications Conference was held in Montpellier, France. The CLA proceedings are published at http://www.ceur-ws.org/Vol-331/ and reflect the diversity of interest in concept lattices by the scientific community with academic papers ranging from the analysis of algorithms in data mining to teaching mathematics using concept lattices.

The CLA conference is structured as a triple peer-review process: peer review of the conference paper, its presentation and, for the best of the CLA papers presented, extended resubmission and review of a journal-length paper.

Forty-eight papers were initially submitted to the CLA 2007 conference and 24 papers were selected for presentation in Montpellier. All papers were peer reviewed by at least three members of the programme committee with the final acceptance decision determined from the reviews and programme chairs. Based on the presentation of the papers at the conference, the best contributions were invited to resubmit an extended version of their papers for this issue. These submissions were again peer reviewed and 6 of the 12 papers submitted for this special volume were accepted for publication.

This collection covers a large range of concept lattice applications that make a contribution to the study and use of concept lattices in the following fields of expertise:

• information browsing and retrieval;

• knowledge acquisition;

• information visualisation;

• unsupervised machine learning;

• knowledge representation;

• logic programming; and

• software engineering.

A common application of concept lattices has been in the area of information browsing and retrieval. The basic notion is that a document is an object and the terms it contains are attributes. Formal concept analysis (Wille and Ganter 1999) can then synthesise a lattice structure that becomes the focus of the interaction with the major advantage that a concept – and its related documents – can be reached via multiple pathways. The original work in this area was pioneered by Godin et al. (1989) and also Carpineto and Romano (1996) with significant improvements and several attempts at commercialisation in the early 2000s by Carpineto and Romano (2004) and Cole et al. (2003).

There are two papers in this volume that offer variations to this continuing application thread. The first, by Emmanuel Nauer and Yannick Toussaint, presents an application called CreChainDo. In CreChainDo a type of interactive learning occurs in conjunction with lattice interactions, the user asserting or denying result relevance which in turn conditions the presentation of the next result set. Nauer and Toussaint's paper could be said to span several discipline areas: interactive information retrieval, knowledge acquisition, and human computer interaction, the use of the concept lattice being the unifying element. The second paper by Sébastien Ferré specialises early work by the author on ‘logical information systems’ (Ferré and Ridoux 2004) to the problem of navigating a photo collection. Ferré's Camelis program builds on earlier work in logical information systems to provide a faceted image navigation and browsing tool that extents the functionality of photo content management software via use of the concept lattice.

One of the enduring features of formal concept analysis is the line diagram: a visualisation of a concept lattice. A line diagram is a specialised form of Hasse diagram labelled with the object extents and the attribute intents. A good example is Figure 1 of the third paper in this collection by Jean Villerd, Sylvie Ranwez, Michel Crampes, and David Carteret, reproduced below.

Figure 1 The concept lattice computed using Galicia from the patent test database (329 objects, 10 attributes).

The line diagram is usually drawn so that its rendering maximises symmetry and minimises edge crossings. Further, the line diagram is usually layered hierarchically from top to bottom. Villerd et al.'s paper breaks with these conventions to explore hybrid visual representations of the concept lattice that use the distance between formal concepts to represent semantic features within an information space. While variations of the line diagram are often frowned upon in the mathematical treatment of formal concept analysis, there is no doubt that hybrid presentations of concept lattices have value in practice, so the editors of the volume consider this paper a particularly important one in the conversation between the theory and application of concept lattices.

Another important thread in the application of concept lattices has been in the maintenance, understanding, and refactoring of software libraries (Snelting 1996). While there are some similarities between free-text and source code, there are also many more complex structural clues about software source code that provide both opportunity and complexity in its analysis. The paper by Gabriela Arévalo, Nicolas Desnos, Marianne Huchard, Christelle Urtado and Sylvain Vauttier provides us with a view of the current state of the art in the formal concept analysis and software engineering area. In their paper, Arévalo et al. present an approach to service classification that relies on the decomposition of the software into three lattice categories including functional signature, interface, and component lattices. Services are then organised among these three lattices in order to identify, navigate, and compose dynamic software components. As modern integrated development environments (IDEs) – formally computer aided software engineering tools – gain in complexity and accelerate programmer efficiency, the ideas presented in this paper provide scope for practical improvements to IDEs that provide a principled method for software component composition in complex object-oriented frameworks.

The first question about formal concept analysis asked by machine learning researchers is, where in the topology of machine learning does formal concept analysis fit? The stock answer is that formal concept analysis is an unsupervised concept clustering technique. However, unsupervised symbolic machine learning presents such a small subset of machine learning that this first question and answer is often the end of the discussion. The penultimate paper in this volume, ‘Inducing decision trees via concept lattices’, is therefore an important bridge from formal concept analysis to supervised machine learning. In their paper, Radim Belohlavek, Bernard De Baets, Jan Outrata, and Vilem Vychodil make clear the connection between concept lattices and decision trees. In their approach, Belohlavek et al. consider a concept lattice (without the least formal concept or bottom element) as a collection of overlapping trees. The construction of a decision tree is then reduced to the problem of selection of one of these trees.

There is a considerable literature in the concept lattice community about the linkages between the use of the concept lattice and knowledge representation in artificial intelligence. The final paper in this volume is a demonstration of one of these linkages between the practice of concept lattices and knowledge representation. Kamel Ben-Khalifa and Susanne Motameny explore a connection between concept lattices and propositional formulas. Their work establishes that the prime implicates of a concept lattice can be considered as a Horn clausal representation. Such a connection is important because it establishes the connection between concept lattices and propositional logic in a way that can contribute to practical implementations of logic programming.

We hope that this collection will impress the casual reader with the diversity of applications of concept lattices and at the same time offer an important resource for researchers directly concerned with concept lattice applications. The production of a volume such as this involves the work and coordination of many individuals, we wish to offer thanks to all who were involved.