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UMP-ST Plug-in: Documenting, Maintaining and Evolving Probabilistic Ontologies Using UnBBayes Framework Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Computing Inferences for Relational Bayesian Networks Based on \(\mathcal {ALC}\) Constructs

Authors : Fabio G. Cozman, Rodrigo B. Polastro, Felipe I. Takiyama, Kate C. Revoredo

Published in: Uncertainty Reasoning for the Semantic Web III

Publisher: Springer International Publishing

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Abstract

Credal \(\mathcal {ALC}\) combines the constructs of the well-known \(\mathcal {ALC}\) logic with probabilistic assessments, so as to let terminologies convey uncertainty about concepts and roles. We present a restricted version of Credal \(\mathcal {ALC}\) that can be viewed as a description language for a class of relational Bayesian networks. The resulting “\(\textsc {cr}\mathcal {ALC}\) networks” offer a simplified and illuminating route both to Credal \(\mathcal {ALC}\) and to relational Bayesian networks. We then describe the implementation, in freely available packages, of approximate variational and lifted exact inference algorithms.

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Footnotes
1
The Kangaroo ontology is distributed with the CEL System at the site http://​lat.​inf.​tu-dresden.​de/​systems/​cel/​.
 
2
We use the following concept of independence: an event \(E\) is independent of a set of events \(\{F_i\}_i\) given a set of events \(\{G_j\}_j\) if \(\mathbb {P}\left( E \cap H'|H'' \right) = \mathbb {P}\left( E|H'' \right) \mathbb {P}\left( H'|H'' \right) \) for any \(H' = \cap _{i \in I} F_i\) and any nonempty \(H'' = (\cap _{j \in J} G_j) \cap (\cap _{k \in K} G_k^c)\), for any subsets of indexes \(I\), \(J\), \(K\).
 
4
The standard specification of KRSS can be found at http://​dl.​kr.​org/​krss-spec.​ps.
 
5
The package is freely available at https://​github.​com/​ftakiyama/​AC-FOVE, where source code and examples can be found.
 
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Metadata
Title
Computing Inferences for Relational Bayesian Networks Based on Constructs
Authors
Fabio G. Cozman
Rodrigo B. Polastro
Felipe I. Takiyama
Kate C. Revoredo
Copyright Year
2014
Book
Uncertainty Reasoning for the Semantic Web III

Print ISBN: 978-3-319-13412-3

Electronic ISBN: 978-3-319-13413-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-13413-0_2

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