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Original Articles

Probabilistic implication bases in FCA and probabilistic bases of GCIs in

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Pages 511-546 | Received 15 May 2016, Accepted 09 Apr 2017, Published online: 08 Aug 2017
 

Abstract

A probabilistic formal context is a triadic context the third dimension of which is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications with respect to probabilistic formal contexts, and provides a construction for a base of implications the probabilities of which exceed a given lower threshold. A comparison between confidence and probability of implications is drawn, which yields the fact that both measures do not coincide. Furthermore, the results are extended towards the lightweight description logic EL with probabilistic interpretations, and a method for computing a base of general concept inclusions the probabilities of which are greater than a pre-defined lower bound is proposed. Additionally, we consider so-called probabilistic attributes over probabilistic formal contexts, and provide a method for the axiomatization of implications over probabilistic attributes.

Acknowledgements

The author thanks Sebastian Rudolph for proof reading and a fruitful discussion, and furthermore the anonymous reviewers for their constructive comments.

Notes

No potential conflict of interest was reported by the author.

1 For two intents X and Y, we say that X is a lower intent-neighbor of Y if XY and there is no intent between X and Y. Furthermore, we denote this as XY.

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