TY - GEN
T1 - A modal characterization theorem for a probabilistic fuzzy description logic
AU - Wild, Paul
AU - Schröder, Lutz
AU - Pattinson, Dirk
AU - König, Barbara
N1 - Publisher Copyright:
© 2019 International Joint Conferences on Artificial Intelligence. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85074944561&partnerID=8YFLogxK
U2 - 10.24963/ijcai.2019/263
DO - 10.24963/ijcai.2019/263
M3 - Conference contribution
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 1900
EP - 1906
BT - Proceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
A2 - Kraus, Sarit
PB - International Joint Conferences on Artificial Intelligence
T2 - 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
Y2 - 10 August 2019 through 16 August 2019
ER -