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Exploring Conceptual Possibilities

Exploring Conceptual Possibilities,10.1007/978-3-642-14197-3_2,Bernhard Ganter

Exploring Conceptual Possibilities  
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Shortly after the ideas of Formal Concept Analysis were first presented by Rudolf Wille in his seminal paper of 1982, one of the basic FCA methods came up: Attribute Exploration. It offers an interactive technique for exploring the possible attribute combinations in a given domain, supporting the search by a powerful and still somewhat peculiar algorithm. Since then, remarkable progress has been made, so that the theoretical foundations of Formal Concept Analysis nowadays are broad and well-established. There are still remarkable research activities in the field, but many of the basic questions are solved and one may wonder what the future directions of research might be. What are worthwhile directions of further investigations on conceptual structures? Suggestions for answers may be obtained from applications of the attribute exploration method, which, when applied to real world situations, often is confronted with problems that require more than the basic technique. Many extensions of the method, with additional features, have been discussed and investigated, mainly because there was demand from the side of applications. Quite in the beginning it was studied how “background knowledge” can be taken into account. An natural question also is how incomplete and imprecise data can be handled. The study of data with symmetries led to an extensions of the method to predicate logic (Horn formulae). More recently, several attempts were made to handle structured data as well. What if the objects under consideration have an inner structure that is related to their attributes? For example, if the objects are molecules, or mathematical items. Or what, if the objects are related to other objects, as it is the case in processes or in causal networks? Then more expressive logics, like description logics, are needed, but that raises difficult questions. And perhaps even more challenging are situations where the data are unreliable, not merely because they are imprecise or incomplete, but because they are provided by many users not all of whom can be trusted. We give an overview of our present knowledge of this theme and indicate some possible goals.
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