Qualitative reasoning in a two-layered framework

0567202 - ÚI 2024 RIV US eng J - Journal Article
Bílková, Marta - Frittella, S. - Kozhemiachenko, D. - Majer, Ondrej
Qualitative reasoning in a two-layered framework.
International Journal of Approximate Reasoning. Roč. 154, March 2023 (2023), s. 84-108. ISSN 0888-613X. E-ISSN 1873-4731
R&D Projects: GA ČR(CZ) GA22-01137S
EU Projects: European Commission(XE) 101007627 - MOSAIC
Institutional support: RVO:67985807 ; RVO:67985955
Keywords : Qualitative probabilities * Comparative belief * Two-layered modal logics * Gödel logic * Belnap–Dunn logic * Paraconsistent logics
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 3.9, year: 2022
Method of publishing: Limited access
https://dx.doi.org/10.1016/j.ijar.2022.12.011

The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a unary belief modality B that connects the inner layer to the outer one where the reasoning is formalised by means of Gödel logic. We design their Hilbert-style axiomatisations and prove their completeness. In the second part, we discuss the paraconsistent generalisations of the logics for qualitative uncertainty that take into account the case of the available information being contradictory or inconclusive.
Permanent Link: https://hdl.handle.net/11104/0338479