@inproceedings{c56e710ddef04e2989bae9cb74c072a3,
title = "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.",
author = "Paul Wild and Lutz Schr{\"o}der and Dirk Pattinson and Barbara K{\"o}nig",
note = "Publisher Copyright: {\textcopyright} 2019 International Joint Conferences on Artificial Intelligence. All rights reserved.; 28th International Joint Conference on Artificial Intelligence, IJCAI 2019 ; Conference date: 10-08-2019 Through 16-08-2019",
year = "2019",
doi = "10.24963/ijcai.2019/263",
language = "English",
series = "IJCAI International Joint Conference on Artificial Intelligence",
publisher = "International Joint Conferences on Artificial Intelligence",
pages = "1900--1906",
editor = "Sarit Kraus",
booktitle = "Proceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019",
address = "United States",
}