Implications over Probabilistic Attributes
Research output: Contribution to book/conference proceedings/anthology/report › Conference contribution › Contributed › peer-review
Contributors
Abstract
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.
Details
Original language | English |
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Title of host publication | Formal Concept Analysis |
Editors | Karell Bertet, Daniel Borchmann, Peggy Cellier, Sébastien Ferré |
Publisher | Springer, Berlin [u. a.] |
Pages | 168-183 |
Number of pages | 16 |
Publication status | Published - 13 Jun 2017 |
Peer-reviewed | Yes |
Publication series
Series | Lecture Notes in Computer Science, Volume 10308 |
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ISSN | 0302-9743 |
External IDs
Scopus | 85021205704 |
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ORCID | /0000-0003-0219-0330/work/153109397 |