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arXiv · 2203.01060

Reasoning with belief functions over Belnap--Dunn logic

Marta Bílková·Sabine Frittella·Daniil Kozhemiachenko·Ondrej Majer·Sajad Nazari
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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.

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Marta Bílková, Sabine Frittella, Daniil Kozhemiachenko, Ondrej Majer, Sajad Nazari. 2022-03-02. Reasoning with belief functions over Belnap--Dunn logic. https://doi.org/10.1016/j.apal.2023.103338

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