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Abstract. This lecture offers an approach of developing an order-theoretic structure theory of convex continuum structures. The chosen approach is based on convex continua and their subcontinua as primitive notions.
 
In a first step linear and circular continuum structures are defined as ordered sets and concretized by a real number model. Then 'points' are deduced as limits of continua by methods of Formal Concept Analysis. The continuum structures extended by those points are analysed and represented by an enlarged real number model.
 
A second step offers an approach to an order-theoretic structure theory of two-dimensional convex continuum structures. The chosen approach is based on convex planar continua and their subcontinua as primitive notions. The convex planar continua are mathematized and represented by ordered sets and then concretized by a real number model. Then again 'points' are deduced as limits of continua by more elaborated methods of Formal Concept Analysis. The continuum structures extended by those points are analysed and represented by an enlarged real number model.
 
As an outlook further research will be sketched to understand the development of mathematizing higher dimensional continuum structures.

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Abstract. In a previous paper, we have introduced an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the assertional part and by a domain expert. This approach, called knowledge base completion, was based on an extension of attribute exploration to the case of partial contexts. The present paper recalls this approach, and then addresses usability issues that came up during first experiments with a preliminary implementation of the completion algorithm. It turns out that these issues can be addressed by extending the exploration algorithm for partial contexts such that it can deal with implicational background knowledge.

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Abstract. In knowledge representations and reasoning systems, diagrams have many practical applications and are used in numerous settings. Indeed, it is widely accepted that diagrams are a valuable aid to intuition and help to convey ideas and information in a clear way. On the other side, logicians have viewed diagrams as informal tools, but which cannot be used in the manner of formal argumentation. Instead, logicians focused on symbolic representations of logics. Recently, this perception was overturned in the mid 1990s, first with seminal work by Shin on an extended version of Venn diagrams. Since then, certainly a growth in the research field of formal reasoning with diagrams can be witnessed. This paper discusses the evolution of formal diagrammatic logics, focusing on those systems which are based on Euler and Venn-Peirce diagrams, and Peirce’s existential graphs. Also discussed are some challenges faced in the area, some of which are specifically related to diagrams.

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Abstract. I use the term logical and relational learning (LRL) to refer to the subfield of machine learning and data mining that is concerned with learning in expressive logical or relational representations. It is the union of inductive logic programming, (statistical) relational learning and multi-relational data mining and constitutes a general class of techniques and methodology for learning from structured data (such as graphs, networks, relational databases) and background knowledge. During the course of its existence, logical and relational learning has changed dramatically. Whereas early work was mainly concerned with logical issues (and even program synthesis from examples), in the 90s its focus was on the discovery of new and interpretable knowledge from structured data, often in the form of rules or patterns. Since then the range of tasks to which logical and relational learning has been applied has significantly broadened and now covers almost all machine learning problems and settings. Today, there exist logical and relational learning methods for reinforcement learning, statistical learning, distance- and kernel-based learning in addition to traditional symbolic machine learning approaches. At the same time, logical and relational learning problems are appearing everywhere. Advances in intelligent systems are enabling the generation of high-level symbolic and structured data in a wide variety of domains, including the semantic web, robotics, vision, social networks, and the life sciences, which in turn raises new challenges and opportunities for logical and relational learning.

This talk will provide an introduction to logical and relational learning, which shall focus on some of the underlying foundations that are of interest to formal concept analysis. This includes the notions of coverage (or matching), generalization and subsumption, the relationships to mining and learning in graphs, and of course, the difficulties to define closures using relational logic and graphs. The talk will be illustrated using some examples of well-known logical and relational learning settings, approaches and applications.

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Abstract. Concept lattices of real world data are usually rather poorly structured, in contrast to lattices arising from mathematical data. However, the math-based structures are useful for representation, and it is therefore important to access their structures. Many of them have symmetries, and it is possible to use these for the simplification algorithms and computations. The idea of a concept lattice "modulo symmetries" has been invented decades ago, but recently we encountered more situations were they are of interest. New algorithms and implementations make the study of advanced examples possible.

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Abstract. Formal concept analysis (FCA) has been successfully used in several Computer Science fields such as databases, software engineering, and information retrieval, and in many domains like medicine, psychology, linguistics and ecology.
In data warehouses, users exploit data hypercubes (i.e., multi-way tables) mainly through online analytical processing (OLAP) techniques to extract useful information from data for decision support purposes.
Many topics have attracted researchers in the area of data warehousing: data warehouse design and multidimensional modeling, efficient cube computation and materialization, physical data organization, query optimization and approximation, discovery-driven data exploration as well as cube compression and mining. Recently, there has been an increasing interest to apply or adapt data mining approaches and advanced statistical analysis techniques for extracting knowledge (e.g., outliers, clusters, rules, closed n-sets) from multidimensional data. Such approaches or techniques cover (but are not limited to) FCA, cluster analysis, principal component analysis, log-linear modeling, and non-negative multi-way array factorization.
Since data cubes rely on dimensions (i.e., analysis axes) with their associated hierarchy, and since cells contain consolidated (e.g., mean value), multidimensional and temporal data, such facts lead to challenging research issues in mining data cubes. In this talk, we will present an overview of related work and show how FCA theory (with possible extensions) can be used to extract valuable and actionable knowledge from data warehouses.

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Abstract. The 20th Century has seen a very important revival of the formal studies of temporal concepts. The most important contribution to the modern logic of time was made in the 1950s and 1960s by A. N. Prior (1914–1969). In his endeavours, Prior was greatly inspired by ancient and medieval thinkers and especially their work on time and logic.

Prior pointed out that when discussing the temporal aspects of reality we use two different conceptual frameworks, the A-concepts (corresponding to dynamic time) and the B-concepts (corresponding to static time). He logically analysed the tension between A-concepts and B-concepts, and he demonstrated that there are four different ways to answer the fundamental question about the nature of the tension between A- and B-concepts.

In addition, using the idea of branching time Prior demonstrated that there are models of time which are logically consistent with his ideas of free choice and indeterminism. It turns out that this discussion is closely related to the analysis of the tension between A- and B-concepts.

After Prior’s founding work in temporal logic, a number of important concepts have been studied within this framework. The introduction of time into logic has led to the development of formal systems which are particularly well suited to representing and studying temporal phenomena such as program execution, temporal databases, and argumentation in natural language.

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Abstract. Traditionally, since it was coined in the early 17th century, the word “ontology” has been used to name a field of metaphysics as well as distinct metaphysical doctrines. Recently, the word “ontology” occurs with increasing frequency in the information sciences, and also in other fields that have been subjected to ‘informatisation’ such as computational biology. In all these fields however, the word “ontology” is being used with different meanings, and moreover, often the meaning of the word “ontology” is not made explicit. Given the apparent centrality and significance of the word “ontology” in the contemporary information sciences, this terminological indeterminateness is a problem that warrants an investigation. Hence, an attempt is made to (a) identify the different meanings of the word “ontology” as used in the information sciences, (b) identify the reasons for the multiplicity of meanings, and (c) explore the relationship between philosophy and information sciences with respect to ontology – to determine whether (philosophical) ontology can or actually does inform the notions of ontology in the information sciences. In conclusion, some implications are discussed regarding the relation between Formal Concept Analysis and ontology.