A Fuzzy Modal Logic for Belief Functions
Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence. Pages 723-731.
Abstract
In this paper we introduce a new logical approach to reason explicitly about Dempster-Shafer belief functions. We adopt the following view: one just starts with Boolean formulas and a belief function on them; the belief of is taken to be the truth degree of the (fuzzy) proposition standing for “is believed”. For our complete axiomatization (Hylbert-style) we use one of the possible definitions of belief, namely as probability of (modal) necessity. This enables us to define a logical system combining the modal logic S5 with an already proposed fuzzy logic approach to reason about probabilities. In particular, our fuzzy logic is the logic Ł which puts Lukasiewicz and Product logics together.
@inproceedings{ijcai2001p99,
title = {A Fuzzy Modal Logic for Belief Functions},
author = {Godo, Lluís and Hájek, Petr and Esteva, Francesc},
booktitle = {Proceedings of the Seventeenth International Joint Conference on
Artificial Intelligence, {IJCAI-01}},
publisher = {International Joint Conferences on Artificial Intelligence},
pages = {723--731},
year = {2001},
url = {https://ijcai.org/proceedings/2001/99},
}
TY - CPAPER TI - A Fuzzy Modal Logic for Belief Functions AU - Godo, Lluís AU - Hájek, Petr AU - Esteva, Francesc T2 - Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI-01 PB - International Joint Conferences on Artificial Intelligence PY - 2001 SP - 723 EP - 731 UR - https://ijcai.org/proceedings/2001/99 ER -Copied
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