A modal characterization theorem for a probabilistic fuzzy description logic

Wild P, Schröder L, Pattinson D, König B (2019)

Publication Type: Conference contribution

Publication year: 2019

Journal

IJCAI-97 - PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, VOLS 1 AND 2

Publisher: International Joint Conferences on Artificial Intelligence

Book Volume: 2019-August

Pages Range: 1900-1906

Conference Proceedings Title: IJCAI International Joint Conference on Artificial Intelligence

Event location: Macao CN

ISBN: 9780999241141

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.

Authors with CRIS profile

Paul Wild Lehrstuhl für Informatik 8 (Theoretische Informatik) Lutz Schröder Lehrstuhl für Informatik 8 (Theoretische Informatik)

Related research project(s)

Probabilistische Beschreibungslogik als Fragment der Probabilistischen Logik Erster Stufe (ProbDL) April 1, 2011 - April 1, 2014

Involved external institutions

Universität Duisburg-Essen (UDE) DE Germany (DE) Australian National University (ANU) AU Australia (AU)

How to cite

APA:

Wild, P., Schröder, L., Pattinson, D., & König, B. (2019). A modal characterization theorem for a probabilistic fuzzy description logic. In Sarit Kraus (Eds.), IJCAI International Joint Conference on Artificial Intelligence (pp. 1900-1906). Macao, CN: International Joint Conferences on Artificial Intelligence.

MLA:

Wild, Paul, et al. "A modal characterization theorem for a probabilistic fuzzy description logic." Proceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019, Macao Ed. Sarit Kraus, International Joint Conferences on Artificial Intelligence, 2019. 1900-1906.

BibTeX: Download