A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic
Abstract
The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.
Cite
Text
Wild et al. "A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic." International Joint Conference on Artificial Intelligence, 2019. doi:10.24963/IJCAI.2019/263Markdown
[Wild et al. "A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic." International Joint Conference on Artificial Intelligence, 2019.](https://mlanthology.org/ijcai/2019/wild2019ijcai-modal/) doi:10.24963/IJCAI.2019/263BibTeX
@inproceedings{wild2019ijcai-modal,
title = {{A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic}},
author = {Wild, Paul and Schröder, Lutz and Pattinson, Dirk and König, Barbara},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2019},
pages = {1900-1906},
doi = {10.24963/IJCAI.2019/263},
url = {https://mlanthology.org/ijcai/2019/wild2019ijcai-modal/}
}