Implications over Probabilistic Attributes

  • Francesco Kriegel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10308)


We consider the task of acquisition of terminological knowledge from given assertional data. However, when evaluating data of real-world applications we often encounter situations where it is impractical to deduce only crisp knowledge, due to the presence of exceptions or errors. It is rather appropriate to allow for degrees of uncertainty within the derived knowledge. Consequently, suitable methods for knowledge acquisition in a probabilistic framework should be developed.

In particular, we consider data which is given as a probabilistic formal context, i.e., as a triadic incidence relation between objects, attributes, and worlds, which is furthermore equipped with a probability measure on the set of worlds. We define the notion of a probabilistic attribute as a probabilistically quantified set of attributes, and define the notion of validity of implications over probabilistic attributes in a probabilistic formal context. Finally, a technique for the axiomatization of such implications from probabilistic formal contexts is developed. This is done is a sound and complete manner, i.e., all derived implications are valid, and all valid implications are deducible from the derived implications. In case of finiteness of the input data to be analyzed, the constructed axiomatization is finite, too, and can be computed in finite time.


Knowledge acquisition Probabilistic formal context Probabilistic attribute Probabilistic implication Knowledge base 



The author gratefully thanks the anonymous reviewers for their constructive hints and helpful remarks.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

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