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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2210.09095 |
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| _version_ | 1866916159814631424 |
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| author | Bilkova, Marta Frittella, Sabine Kozhemiachenko, Daniil Majer, Ondrej |
| author_facet | Bilkova, Marta Frittella, Sabine Kozhemiachenko, Daniil Majer, Ondrej |
| contents | 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 $\Be$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09095 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Qualitative reasoning in a two-layered framework Bilkova, Marta Frittella, Sabine Kozhemiachenko, Daniil Majer, Ondrej Logic 03B42 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 $\Be$ 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. |
| title | Qualitative reasoning in a two-layered framework |
| topic | Logic 03B42 |
| url | https://arxiv.org/abs/2210.09095 |