Two-Layered Logics for Paraconsistent Probabilities

0580808 - ÚI 2024 RIV CH eng C - Conference Paper (international conference)
Bílková, Marta - Frittella, S. - Kozhemiachenko, D. - Majer, Ondrej
Two-Layered Logics for Paraconsistent Probabilities.
Logic, Language, Information, and Computation. Cham: Springer, 2023 - (Hansen, H.; Scedrov, A.; de Queiroz, R.), s. 101-117. Lecture Notes in Computer Science, 13923. ISBN 978-3-031-39783-7.
[WoLLIC 2023: Workshop on Logic, Language, Information and Computation /29./. Halifax (CA), 11.07.2023-14.07.2023]
R&D Projects: GA ČR(CZ) GA22-01137S
EU Projects: European Commission(XE) 101007627 - MOSAIC
Institutional support: RVO:67985807 ; RVO:67985955
Keywords : two-layered logics * Łukasiewicz logic * non-standard probabilities * paraconsistent logics * constraint tableaux
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
https://doi.org/10.1007/978-3-031-39784-4_7

We discuss two-layered logics formalising reasoning with paraconsistent probabilities that combine the Łukasiewicz [0,1]-valued logic with Baaz Delta operator and the Belnap–Dunn logic. The first logic formalises a ‘two-valued’ approach where each event ϕ has independent positive and negative measures that stand for, respectively, the likelihoods of ϕ and ¬ϕ. The second logic that we introduce here corresponds to ‘four-valued’ probabilities. There, ϕ is equipped with four measures standing for pure belief, pure disbelief, conflict and uncertainty of an agent in ϕ. We construct faithful embeddings of and into one another and axiomatise using a Hilbert-style calculus. We also establish the decidability of both logics and provide complexity evaluations for them using an expansion of the constraint tableaux calculus for L.
Permanent Link: https://hdl.handle.net/11104/0349571