Probabilistic Description Logics for Subjective Uncertainty

Víctor Gutiérrez-Basulto, Jean Christoph Jung, Carsten Lutz, Lutz Schröder

JAIR 2017 pp. 1-66

doi:10.1613/JAIR.5222 /jair/2017/gutierrezbasulto2017jair-probabilistic/

Abstract

We propose a new family of probabilistic description logics (DLs) that, in contrast to most existing approaches, are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to certain popular combinations of DLs with temporal logic and are well-suited for capturing subjective probabilities. Our main contribution is a detailed study of the complexity of reasoning in the new family of probabilistic DLs, showing that it ranges from PTIME for weak variants based on the lightweight DL EL to undecidable for some expressive variants based on the DL ALC.

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Text

Gutiérrez-Basulto et al. "Probabilistic Description Logics for Subjective Uncertainty." Journal of Artificial Intelligence Research, 2017. doi:10.1613/JAIR.5222

Markdown

[Gutiérrez-Basulto et al. "Probabilistic Description Logics for Subjective Uncertainty." Journal of Artificial Intelligence Research, 2017.](https://mlanthology.org/jair/2017/gutierrezbasulto2017jair-probabilistic/) doi:10.1613/JAIR.5222

BibTeX

@article{gutierrezbasulto2017jair-probabilistic,
  title     = {{Probabilistic Description Logics for Subjective Uncertainty}},
  author    = {Gutiérrez-Basulto, Víctor and Jung, Jean Christoph and Lutz, Carsten and Schröder, Lutz},
  journal   = {Journal of Artificial Intelligence Research},
  year      = {2017},
  pages     = {1-66},
  doi       = {10.1613/JAIR.5222},
  volume    = {58},
  url       = {https://mlanthology.org/jair/2017/gutierrezbasulto2017jair-probabilistic/}
}