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

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Uncertainty Reasoning for the Semantic Web III (URSW 2012, URSW 2011, URSW 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8816))

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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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Notes

  1. 1.

    The Kangaroo ontology is distributed with the CEL System at the site http://lat.inf.tu-dresden.de/systems/cel/.

  2. 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 \(I\), \(J\), \(K\).

  3. 3.

    The package is freely available, in compressed form, at the site http://sites.poli.usp.br/pmr/ltd/Software/CRALC/inf-cralc-v21may2012.zip.

  4. 4.

    The standard specification of KRSS can be found at http://dl.kr.org/krss-spec.ps.

  5. 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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Acknowledgements

The first author was partially supported by CNPq. The second author was supported by FAPESP. The work reported here has received substantial support by FAPESP grant 2008/03995-5.

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Authors and Affiliations

  1. Universidade de São Paulo, Av. Prof. Mello Moraes, 2231, São Paulo–SP, Brazil

    Fabio G. Cozman, Rodrigo B. Polastro & Felipe I. Takiyama

  2. Departamento de Informática Aplicada, UNIRIO, Av. Pasteur, 458, Rio de Janeiro–RJ, Brazil

    Kate C. Revoredo

Authors
  1. Fabio G. Cozman
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  2. Rodrigo B. Polastro
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  3. Felipe I. Takiyama
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  4. Kate C. Revoredo
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Correspondence to Fabio G. Cozman .

Editor information

Editors and Affiliations

  1. University of Zaragoza, Zaragoza, Spain

    Fernando Bobillo

  2. Universidade de Brasília, Brasília, Brazil

    Rommel N. Carvalho

  3. George Mason University, Fairfax, Virginia, USA

    Paulo C.G. Costa

  4. Università degli Studi di Bari, Bari, Italy

    Claudia d'Amato

  5. Università degli Studi di Bari, Bari, Italy

    Nicola Fanizzi

  6. George Mason University, Fairfax, Virginia, USA

    Kathryn B. Laskey

  7. MITRE Corporation, McLean, Virginia, USA

    Kenneth J. Laskey

  8. University of Oxford, Oxford, United Kingdom

    Thomas Lukasiewicz

  9. National University of Ireland, Galway, Ireland

    Matthias Nickles

  10. Goldman Sachs, Washington, District of Columbia, USA

    Michael Pool

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Cozman, F.G., Polastro, R.B., Takiyama, F.I., Revoredo, K.C. (2014). Computing Inferences for Relational Bayesian Networks Based on \(\mathcal {ALC}\) Constructs. In: Bobillo, F., et al. Uncertainty Reasoning for the Semantic Web III. URSW URSW URSW 2012 2011 2013. Lecture Notes in Computer Science(), vol 8816. Springer, Cham. https://doi.org/10.1007/978-3-319-13413-0_2

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