Reasoning with belief functions over Belnap--Dunn logic
Logic
2023-07-19 v2
Abstract
We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and belief functions in two ways. First, using a calculus of linear inequalities, akin to the one presented in~\cite{FaginHalpernMegiddo1990}. Second, as a two-layered modal logic wherein reasoning with evidence (the outer layer) utilises paraconsistent expansions of \L{}ukasiewicz logic. The second approach is inspired by~\cite{BaldiCintulaNoguera2020}. We prove completeness for both kinds of calculi and show their equivalence by establishing faithful translations in both directions.
Keywords
Cite
@article{arxiv.2203.01060,
title = {Reasoning with belief functions over Belnap--Dunn logic},
author = {Marta Bílková and Sabine Frittella and Daniil Kozhemiachenko and Ondrej Majer and Sajad Nazari},
journal= {arXiv preprint arXiv:2203.01060},
year = {2023}
}