Reasoning with belief functions over Belnap–Dunn logic

0582922 - ÚI 2025 eng J - Článek v odborném periodiku
Bílková, Marta - Frittella, S. - Kozhemiachenko, D. - Majer, Ondrej - Nazari, S.
Reasoning with belief functions over Belnap–Dunn logic.
Annals of Pure and Applied Logic. Online July 2023 (2024), č. článku 103338.
Grant CEP: GA ČR(CZ) GA22-01137S
GRANT EU: European Commission(XE) 101007627 - MOSAIC
Institucionální podpora: RVO:67985807
Klíčová slova: Belief functions * Belnap–Dunn logic * Two-layered modal logics * Paraconsistent logics * Łukasiewicz logic
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.apal.2023.103338

We design an expansion of Belnap–Dunn logic with belief and plausibility functions that allows non-trivial reasoning with contradictory 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 [23]. Second, as a two-layered modal logic wherein reasoning with evidence (the outer layer) utilises paraconsistent expansions of Łukasiewicz logic. The second approach is inspired by [3]. We prove completeness for both kinds of calculi and show their equivalence by establishing faithful translations in both directions.
Trvalý link: https://hdl.handle.net/11104/0350964